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Question 1 :
State whether the following statements are True or False.<br/>If E=0, at all points of a closed surface,&#160;The electric flux through the surface is zero.

Question 2 :
A charged body is brought near an uncharged gold leaf&#160;electroscope. What will be your observation if the body is&#160;charged?

Question 3 :
A gold leaf electroscope is given a positive charge so that its leaves diverge. How is the divergence of leaves affected, when a glass rod rubbed with silk is rolled on the disc of electroscope?

Question 5 :
Two conducting charged spheres $X$ and $Y$ having unequal charges are connected by the wire. Which of the following is true?

Question 6 :
A charge $q_1$ exerts a force of $45N$ on a charge of $q_{2}=10^{-5} C$ located at a point $0.2m$ from $q_{1}$. The magnitude of $q_{1}$ is

Question 7 :
State whether true or false :Gauss law is applicable only when there is a symmetric distribution of charge.

Question 8 :
If the number of electric lines of force emerging out of a closed surface is 1000, then the charge enclosed by the surface is

Question 9 :
A negatively charged particle is situated on a straight line joining two other stationary particles each having charge $ +q$. The direction of the motion of the negatively charged particle will depend on:

Question 10 :
<p class="wysiwyg-text-align-left">A charge $Q\ &#160;\mu C$ is placed at the centre of a cube. The flux coming out from any surface will be :<br/></p>

Question 11 :
Negative electric flux indicates that electric lines of force are directed

Question 12 :
State whether true or false :Electric field calculated by a Gauss law is the field due to only those charges which are enclosed inside the Gaussian surface.

Question 13 :
A charge + Q is located in space at the point $(x=1m,y=10m,z=5m)$. What is the total electric flux that passes through the yz-plane?

Question 14 :
<span class="wysiwyg-font-size-small"><span class="wysiwyg-font-size-small"><p class="wysiwyg-text-align-left">A charge of $5 C$ is placed at the centre of a spherical gaussian surface of radius $5 cm$. The electric flux through the surface is $\dfrac{1}{\varepsilon _{0}}$ times of</p>

Question 15 :
<span class="wysiwyg-font-size-small"><span class="wysiwyg-font-size-small">Another unit for the quantity having the unit $\dfrac{C^2 }{Nm^2}$ is:

Question 17 :
The process due to which an uncharged body acquires electric charges when held near a charged body is called :<br/>

Question 18 :
Electrical charge can be transferred from a charged object to another through

Question 20 :
Some materials have electrons that are tightly bound to the nucleus and are not free to travel within the substance. These materials are called .............

Question 22 :
Two spheres of radii 2 cm and 3 cm have equal surface charge density. Calculate the ratio of their charges.

Question 23 :
A gold leaf electroscope is given a positive charge so that its leaves diverge. How is the divergence of leaves affected, when a negatively charged rod is brought near its&#160;disc?

Question 24 :
The materials that do not allow flow of electron through them are known as :

Question 26 :
Three identical charges, each having a value $1.0 \times 10 ^ { - 3 } \mathrm { C }$are placed at the corners of an equilateral triangle of side 20 cm Find the potential at the center of the triangle

Question 30 :
If the electric force between two unknown charges is attractive, identify which of the following statement must be true?<br/>

Question 32 :
Two charges are placed at certain distance apart. A metallic sheet is placed between them. What will happen to the force between the charges?

Question 33 :
When a negative charge is taken at a height from earth's surface, then its potential energy:

Question 34 :
Assertion: Gauss's law show diversion when inverse square law is not obeyed. Reason: Gauss's law is a consequence of conservation of charges.

Question 36 :
A small sphere of mass $m$ and electric charge $q$, is suspended by a light thread. A second sphere carrying a charge $q_2$ is placed directly below the first sphere at a distance $'d' $ away. Then :

Question 37 :
What will bethe effect on the divergence of the leaves of aunchargedgold leaf electroscope onbringing a negatively charged rod near electroscope?

Question 40 :
When a glass rod is rubbed with silk cloth, it acquires positive charge because:

Question 42 :
In an external electric field, the field line of force represent:<br/>

Question 43 :
Which of the following devicesis used to detect the presences of a charge on a body?<br>

Question 44 :
<span class="wysiwyg-font-size-small"><span class="wysiwyg-font-size-small"><p class="wysiwyg-text-align-left">The angle between the electric dipole moment and the electric field strength due to it, on the equatorial line is :</p>

Question 45 :
You are provided with a negatively charged gold leaf electroscope. State and explain what happens when an uncharged metal rod is brought near the disc of electroscope.

Question 46 :
A charge is placed at the centre of a cube. The electric flux through one face of the cube is :<br/>

Question 47 :
Which of the following may be discontinuous across a charged conducting surface?

Question 49 :
&#160;If E=0, at all points of a closed surface.&#160;The total charge enclosed by the surface is zero.

Question 51 :
<table class="table table-bordered"><tbody><tr><td>&#160;i. $\sigma _a$</td><td>&#160;m. $\dfrac{q_a + q_b}{4 \pi R^2}$</td></tr><tr><td>&#160;ii. $\sigma_b$</td><td>&#160;n. $\dfrac{-q_a}{4 \pi a^2}$</td></tr><tr><td>&#160;iii. $\sigma_R$</td><td>&#160;o. $\dfrac{-q_b}{4 \pi b^2}$</td></tr></tbody></table>Match the table.

Question 52 :
Assertion: Charge is quantized because only integral number of electrons can be transferred. Reason: There is no possibility of transfer of some fraction of electron.

Question 53 :
In Region of Electric field Given by $\vec{E} = (Ax + B) \hat{i}$. Where $A = 20$ unit and $B = 10$ unit. If Electric potential at $x = 1\,m$ is $V_1$ and at $x = -5 \,m$ is $V_2$. Then $V_1 - V_2$ is equal to

Question 55 :
A and B are two points on the axis and the perpendicular bisector respectively of an electric dipole. A and B are far away from the dipole and at equal distances from its centre. The fields at A and B i.e. $\overrightarrow { { E }_{ A } } \quad and\overrightarrow { { E }_{ B } }$ are respectively such that

Question 58 :
Two point charges + 8 q and -2q are located at x = 0 and x=L respectively. The location of a point on the x axis at which the net electric field due to these two point charge is zero is -

Question 59 :
Two point charges placed at a certain distance r in air exert a force F on each other. The distance r at which these charges will exert the same force in medium if dielectric constant k is given by

Question 60 :
Assertion: For a charged particle moving from point P to point Q, the net work done by an electrostatic field on the particle is independent of the path connecting point P to point Q. Reason: The net work done by a conservative force on an object moving along a closed loop is zero.

Question 61 :
<p>A charged particle is released from rest in a region of steady and uniform electric and magnetic field which are parallel to each other. The nature of light<br/></p>

Question 63 :
As per Gauss law<br>$\int E.dS \ =\large{ \frac{q_{in}}{\epsilon_0}}$<br>Which of the following is true about this

Question 64 :
The electric field in a region of space is given by $E = 5i + 2j\ N/C$. Determine the electric flux due to this field through an area $2m^{2}$ lying in the $YZ$ plane:

Question 66 :
Two identical conducting small spheres are placed with their&#160;centres&#160;$0.3 m$ apart. One is given a charge of $12.0 nC$ and the other a charge of $-18.0 nC$.&#160;Find the electric force exerted by one sphere on the other?

Question 67 :
Under the influence of the Coulomb field of charge $+Q$, a charge $-q$ is moving around it in an elliptical orbit. Find out the correct statements.

Question 68 :
A point charge q produces an electric field of magnitude $2\ N\ C^{-1}$ at a point distance $0.25\ m$ from it. Find the value of charge.

Question 70 :
<span class="wysiwyg-font-size-small"><span class="wysiwyg-font-size-small"><p class="wysiwyg-text-align-left">Two particles with identical positive charges and a separation of $2.5\times 10^{-2}m$ are released from rest. Immediately after their release, particle 1 has acceleration whose magnitude is $4\times 10^{3}ms^{-2}$. Particle 1 has a mass of $9\times 10^{-6}kg$. Then each of the particle has charge of :<br/></p>

Question 71 :
Charges $\theta_1$ and $\theta_2$ lie inside and out side respectively for a closed surface s. Let E be the field at a point on S and $\phi$ be flux of E over S

Question 72 :
A spherical volume has a uniformly distributed charge density $2\times 10^{-4} Cm^{-3}$. The electric field at a point inside the volume at a distance 4.0 cm from the centre is :

Question 73 :
An oil drop is negatively charged and weights $5 \times 10^{-4} N$ .The drop is suspended in an electric field intensity of $ 2.6 \times 10^4 N/C$ .The number of electrons the oil drop is in $x \times10^{10}$. Then $x$ is

Question 74 :
The electric charge developed on glass rod rubbed with silk cloth is different from the charge developed on ebonite rod rubbed with fur.

Question 75 :
A point charge of value $10^{-7}\ C$ is situated at the centre of cube of $1\ m$ side. The electric flux through its total surface area is:

Question 76 :
If there is only one type of charge in the universe, then what is the flux to the entire universe.<br/>($\vec { E } \rightarrow $ Electric field, $\vec { ds } \rightarrow $ Area vector)

Question 77 :
Gaussian surfaces for a point charge and a charged sphere are

Question 78 :
An attractive force of $9$ N acts between $+5$ C and $-5$ C at some distance. These charges are allowed to touch each other and are then again placed at their initial position. The force acting between them will be :

Question 79 :
Assertion: A positive point charge initially at rest in a uniform electric field starts moving along electric lines of force. (Neglect all other forces except electric forces) Reason: Electric lines of force represent path of charged particle which is released from rest in it.

Question 80 :
A charge q is moving with a velocity $\bar v_1$ = $1\hat i m/s$ at a point in a magnetic field and experiences a force $\bar F_1 = q[-1\hat j + 1\hat k]N$. If the charge is moving with a velocity $\bar v_2 = 1\hat j m/s$ at the same point, it experiences a force $\bar F_2 = q[1\hat i - 1\hat k] N$. The magnetic induction $\bar B$ at that point is

Question 81 :
An imaginary, closed spherical surface $S$ of radius $R$ is centered on the origin. A positive charge $+q$ is originally at the origin and electric flux through the surface is $\phi_{E}$. Three additional charges are now added along the $x$ axis: $-3q$ at $x =-\dfrac {R}{2}, +5q$ at $x = \dfrac {R}{2}$ and $4q$ at $x = \dfrac {3R}{2}$. The flux through $S$ is now :

Question 82 :
An example in which light emitting diodes are used is :

Question 83 :
If<b>&#160;</b>the force between two charged objects separated by a distance d&#160;is to be&#160;left unchanged even though the charge on one of the objects is halved,&#160;keeping other the same, the new distance of separation becomes :

Question 85 :
<span class="wysiwyg-font-size-small"><span class="wysiwyg-font-size-small"><p class="wysiwyg-text-align-left">Two identical charged spheres are suspended by strings of equal length and the strings make certain angle with each other. When<span class="wysiwyg-font-size-small"><span class="wysiwyg-font-size-small">suspended in a liquid of density <span class="wysiwyg-font-size-small"><span class="wysiwyg-font-size-small">$400\ kg/m^{3}$<span class="wysiwyg-font-size-xx-small"><span class="wysiwyg-font-size-xx-small"> <span class="wysiwyg-font-size-small"><span class="wysiwyg-font-size-small">, theangle between the threads remains the same. If the density of the material of the sphere is<span class="wysiwyg-font-size-small"><span class="wysiwyg-font-size-small">$1600\ kg/m^{3}$<span class="wysiwyg-font-size-xx-small"><span class="wysiwyg-font-size-xx-small"> <span class="wysiwyg-font-size-small"><span class="wysiwyg-font-size-small">, the dielectric constant of the liquid:</p>

Question 86 :
Two positive point charges $q$ are placed at &#160;$(a,0)$ and $(-a,0)$. A third positive charge $q_o$ is placed at $(0,y)$. For what value of $y$, the force on $q_o$ is maximum?

Question 87 :
Two point charges of $+3\mu C$ and $+4\mu C$ repel each other with a force of $10N$. If each is given an additional charge of $-6\mu C$, the new force is:

Question 88 :
An insulated sphere of radius $R$ has a uniform volume charge density $\rho$. The electric field at a point $P$ inside the sphere at a distance $r$ from the centre is

Question 89 :
An electric dipole, consisting of two opposite charges of magnitude $ 2\times 10^{-6}$ C each separated by a distance 3 cm is placed in an electric field of magnitude $2 \times 10^{5}$ N/C along the direction making $90^0$ with the field.&#160;Torque acting on the dipole is :

Question 90 :
Assertion: Gauss theorem can be applied only for a closed surface. Reason: Electric flux can be obtained passing from an open surface also.

Question 91 :
Two solid spheres, both of radius $5 cm$, carry identical total charges of $2\mu C$. Sphere $A$ is a good conductor.Sphere $B$ is an insulator, and its charge is distributed&#160;uniformly throughout its volume.<br/>How do the magnitudes of the electric&#160;fields they separately create at radius 4 cm compare?

Question 92 :
Force between two charges $q_1$ and $q_2$ separated by a distance r is proportional to $q _ { 1 } q _ { 2 } / r ^ { 2 }$ . Proportionality constant is

Question 93 :
If one penetrates a uniformly charged solid sphere, the electric field $E$:<br/>

Question 94 :
What is the new force of repulsion between A and B?

Question 95 :
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" alt=""/>A solid sphere having uniform charge density $\rho$ and radius R is shown in figure. A spherical cavity of radius $\dfrac{R}{2}$ is hollowed out. What is potential of O? (Assuming potential at infinity to be zero).

Question 97 :
A charge $\mathrm{Q}$ is placed at each of the opposite comers of a square. A charge $\mathrm{q}$ is placed at each of the other two corners. If the net electrical force on $\mathrm{Q}$ is zero, then $\mathrm{Q}/\mathrm{q}$ equals:<br>

Question 98 :
A charge $Q$ is placed at each of two opposite corners of a square. A charge $q$ is laced at each of the two opposite corners of the square. If the resultant electric field on $Q$ is zero, then

Question 99 :
Assertion: On going away from a point charge or a small electric dipole, electric field decreases at the same rate in both the cases. Reason: Electric field is inversely proportional to square of distance from the charge or on electric dipole.

Question 100 :
<span class="wysiwyg-font-size-small"><span class="wysiwyg-font-size-small"><p class="wysiwyg-text-align-left">The vertices of an equilateral triangle lie on the&#160;circumference of a circle of radius $6 cm$. Charges&#160;each of $3C$ are placed at the vertices. If a charge&#160;of $1C$ is placed at the center of the circle, the&#160;force acting on it is:</p>

Question 101 :
The electric field at a point $2$cm from an infinite line charge of linear charge density $10^{-7}$ $cm^{-1}$ is?

Question 102 :
Using general logic for electric field, the flux of&#160;$\overrightarrow{g}$ through any closed surface is given by :

Question 103 :
Charges Q, 2Q and 4Q are uniformly distributed in three dielectric solid spheres 1, 2 and 3 of radii R/2, R and 2R respectively. If magnitudes of the electric fields at point P at a distance R from the centre of spheres 1, 2 and 3 are $E_1, E_2,$ and $ E_3$ respectively, then:<br/>

Question 104 :
The flux of the electric field due to charges distributed in a sphere of radius $5$ cm is $10$ Vm. What will be the electric flux, through a concentric sphere of radius $10$ cm ?

Question 105 :
Fill in the blanks.<br/>A field normal to the plane of a circular wire n turns and radius r which carries a current I is measured on the axis of the coil at small h distance h from the centre of the coil. This is smaller than the field at the centre by a friction ____

Question 106 :
A particle of mass m and charge -q moves diametrically through a uniformly charged sphere of radius R with total charge Q. The angular frequency of the particle's simple harmonic motion, if its amplitude &lt; R, is given by :

Question 107 :
A solid sphere of radius $R$ has a charge $Q$ distributed in its volume with a charge density $\rho = kr^{a}$, where $k$ and $a$ are constants and $r$ is the distance from its centre. If the electric field at $r = \dfrac {R}{2}$ is $\dfrac {1}{8}$ times that at $r = R$, the value of $a$ is

Question 108 :
Consider an area element $dS$ at a distance $r$from a point P. Let $\hat r$be the unit vector along the outward normal to $dS$.If $\alpha$ is the angle between $\hat r$ and $dS$,the element of the solid angle subtended by the area element at P is defined as

Question 109 :
Two thin rods of length L lie along x-axis, one between $\displaystyle x = \frac{a}{2} &#160;\ \ \ &#160; to &#160; \ \ \ \ \ x = \frac{a}{2} + L$ and the other between $x = \displaystyle -\frac{a}{2} &#160;to &#160;\ \ \ \ \ x = - \frac{a}{2} - L$.<br/>Each rod has positive charge Q distributed uniformly along the length. Find the magnitude of the force which one rod exerts on the other.

Question 110 :
Charges $Q_1$ and $Q_2$ lie inside and outside respectively of a closed surface S. Let E be the field at any point on S and $\psi$ be the flux of E over S.

Question 111 :
The value of distance $r_m$ at which electric field intensity is maximum, is given by :

Question 112 :
Let $E_1(r), E_2(r)$ and $E_3(r)$ be the respective electric fields at a distance r from a point charge Q, an infinitely long wire with constant linear charge density $\lambda$, and an infinite plane with uniform surface charge density $&#160;\sigma $. lf $E_1(r_0) = E_2(r_0) = E_3(r_0)$ at a given distance $r_0$, then :<br/>

Question 113 :
A spherically symmetric charge distribution is characterised by a charge density having the following variation :<br>$p(r)=p_o(1-\frac {r}{R})$ for $r&lt;R$<br>$p(r)=0$ for $r\geqslant R$<br>Where r is the distance from the centre of the charge distribution and $p_o$ is a constant. The electric field at an internal point (r&lt;R) is :

Question 114 :
Two infinitely long parallel conducting plates having surface charge densities$\displaystyle +\sigma$ and$\displaystyle -\sigma$respectively, are separated by a small distance. The medium between the plates is vacuum. If$\displaystyle { \varepsilon }_{ 0 }$is the dielectric permittivity of vacuum then the electric field in the region between the plates is:

Question 117 :
A point charge $q$ is placed at a point on the axis of a non-conducting circular plate of radius $r$ at a distance $R (R &gt;&gt; r)$ from its center. The electric flux associated with the plate is :<br/>

Question 118 :
Find the electric field at a distance $x$ from the centreinside the shell.

Question 119 :
Charges $Q_1$ and $Q_2$ lie inside and outside respectively of a closed surface S. Let E be the field at anypoint on S and $\phi$be the flux of E over S

Question 121 :
A ball of radius R carries a positive charge whose volume charge density depends only on the distance r from the ball's centre as: $\rho=\rho_0(1-\dfrac {r}{R})$ where $\rho_0$ is constant. Assume $\epsilon$ as the permittivity of the ball.<br/>Then the magnitude of the electric field as a function of the distance r outside the ball is given by :

Question 122 :
In a region, volume density of charge varies with the y-coordinate according to the law $\rho = a|y|$. The electric field as a function of distance y is given by $E = \frac {ay^2}{2^n \epsilon_0}$. Value of n is&#160;('a' is a positive constant):

Question 123 :
A point charge +q is placed at the centre of a cube of side L. The electric flux emerging from the cube is-

Question 124 :
The electric field in a region is $E = \displaystyle \frac{5\times 10^3 x}{2}\hat{i} \ NC^{-1} cm^{-1} $. The charge contained inside a cubical volume bounded by the surfaces $x = 0, x = 1, y = 0, y = 1, z = 0, z = 1$ is (where x, y, z are in cm) :

Question 125 :
The magnitude of electric field as a function of the distance r inside the sphere is given by :

Question 126 :
A solid sphere of radius $R$ has a charge $Q$ distributed in its volume with a charge density $\rho =\kappa { r }^{ a }$, where $\kappa$ and $a$ are constants and $r$ is the distance from its centre.<br>If the electric field at $r=\cfrac{R}{8}$ is $\cfrac{1}{8}$ times that at $r=R$, find the value of $a$ .

Question 127 :
Let a total charge $2Q$ be distributed in a sphere of radius $R$, with the charge density given by $\rho(r) = kr$, where $r$ is the distance from the centre. Two charges $A$ and $B$, of $-Q$ each, are placed on diametrically opposite points, at equal distance, a form the centre. If $A$ and $B$ do not experience any force, then:

Question 128 :
An atom is modelled as a point charge of +e at the nucleus with the electron charge distribution, described by the charge density<br/><br/>$\rho=\dfrac{-15 e}{8 \pi a^3}\left ( 1-\dfrac{r^2}{a^2} \right )$ &#160;for &#160;$r &#160;\leq &#160;a &#160;&lt; &#160;0$<br/>$\rho \simeq 0 &#160;$ for $ r&gt;a, $ where 'a' is a constant.<br/>The net charge contained within a sphere of radius r &lt; a is :

Question 129 :
Charges $Q_1$ and $Q_2$ are placed inside and outside respectively of an uncharged conducting shell. Their seperation is r.

Question 131 :
The electric field in a region is radially outward with magnitude $E=\alpha r$. Calculate the charge contained in a sphere of radius R centered at the origin. Calculate the value of the charge if $\alpha =100 Vm^{-2}$ and R=0.30 m.

Question 132 :
An electric charge $q$is placed at the centre of a cube of side $a$ The electric flux throughone of its faces is

Question 133 :
The ratio of the energy required to set up in cube of side 10 cm uniform magnetic field of 4${ Wb/m }^{ 2 }$ and a uniform electric field of $10^{ 6 }V/m$ is:

Question 134 :
A system consists of a thin charged wire ring of radius r and a very long uniformly charged wire oriented along the axis of the ring, with one of its ends coinciding with the center of the ring. The total charge on the ring is q, and the linear charge density on the straight wire is $\lambda$. The interaction force between the ring and the wire is :

Question 135 :
A point charge $q$ is situated at a distance $r$ on axis from one end of a thin conducting rod of length $L$ having a charge $Q$ (Uniformly distributed along its length). The magnitude electric force between the two is _______

Question 137 :
Two charged spheres having radii a and b are joined with a wire then the ratio of electric field $\dfrac{E_a}{E_b}$ on their surface is?

Question 138 :
Electric flux through a surface of area $100\ m^{2}$ lying in the xy plane is (in V-m) if $\vec{E}=\hat{i}+\sqrt{2}\hat{j}+\sqrt{3\hat{k}}$<br/>

Question 139 :
Two thin rods of linear charge density $\lambda$ Cm$^{-1}$ are separated by a distance d metre. The force on unit length of each rod is :

Question 140 :
Assertion: STATEMENT-1 : In a region where uniform electric field exists, the net charge within volume of any size is zero. Reason: STATEMENT-2 : The electric flux within any closed surface in a region of uniform electric field is zero.

Question 141 :
Mathematically, electric flux can $\phi$be represented as:<br><br>$\vec E =$ electric field<br>$\hat n=$ surface normal vector<br>$A=$ surface area

Question 142 :
Eight dipoles of charges of magnitude $q$ are placed inside a cube. Then, the total electric flux coming out of the cube will be

Question 143 :
Let there be a spherically symmetric charge distribution with charge density varying as $\displaystyle \mathrm{p}(\mathrm{r})=\mathrm{p}_{0}(\frac{5}{4}-\frac{\mathrm{r}}{\mathrm{R}})$ upto $\mathrm{r}=\mathrm{R}$, and $\mathrm{p}(\mathrm{r})=0$ for $\mathrm{r}&gt;\mathrm{R}$, where $\mathrm{r}$ is the distance from the origin. The electric field at a distance $\mathrm{r}(\mathrm{r}&lt;\mathrm{R})$ from the origin is given by :<br/>

Question 144 :
Charges $Q_1$ and $Q_2$ lie inside and outside respectively of a closed surface S. Let E be the field at any point on S and $\phi$ be the flux of E over S.

Question 145 :
A sphere of radius R carries charge such that its volume charge density is proportional to the square of the distance from the center. What is the ratio of the magnitude of the electric field at distance 2R from the center to the magnitude of the electric field at a distance of R/2 from the center?

Question 146 :
The total electric flux through a closed surface is equal to

Question 148 :
A semi-circular rod of radius $R$ is charged uniformly with a total charge $Q\ C$. The electric field intensity at the centre of the curvature is<br/>(where $K= \dfrac{1}{4 \pi \epsilon_0}$)<br/>

Question 149 :
The electric field $0.50 m$ from a small sphere with a positive charge of&#160;$7.2\times 10^{5} C$&#160;is

Question 150 :
Compute the electric flux through a square surface of edges $2l$due to a charge $+Q$ whose geometric centre islocated on the x-axis at a perpendicular distance $l$ from the centre of the square.