Question 1 :
Two points {tex} P {/tex} and {tex} Q {/tex} are maintained at the potentials of {tex}10 \mathrm { V } {/tex} and {tex}-4 \mathrm { V } {/tex} , respectively. The work done in moving {tex} \mathrm { } {/tex}{tex}100{/tex} electrons from {tex} P {/tex} to {tex} Q {/tex} is:
Question 2 :
An electric field given by <em>E⃗</em> = 4<em>î</em> − 3(<em>y</em><sup>2</sup> + 2)<em>ĵ</em> pierces Gaussian cube of side 1<em>m</em> placed at origin such that its three sides represents <em>x, y</em> and <em>z</em> axes. The net charge enclosed within the cube is
Question 3 : Two concentric spherical shell of radius <em>R</em> and 2<em>R</em> having initial charges <em>Q</em> and 2<em>Q</em> respectively as shown. On closing the switch <em>S</em> charge flow from outer sphere to earth is <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c3254bec8070e4e15143"/>
Question 4 :
8 drops of equal radius coalesce to form a bigger drop. By what factor the charge and potential change?
Question 5 : In the diagram shown, the charge +<em>Q</em> is fixed. Another charge +2<em>q</em>, is projected from a distance <em>R</em> from the fixed charge. Minimum separation between the two charges if the velocity becomes half of the projected velocity, at this moment is (Assume gravity to be absent) <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c351f1a5a149feab9a80"/>
Question 6 :
A spring block system undergoes vertical oscillations above a large horizontal metal sheet with uniform positive charge. The time period of the oscillation is <em>T</em>. If the block is given a charge <em>Q</em>, its time period of oscillation
Question 7 :
Coulomb's law relates two charges and distance between them describing the electric force as being
Question 8 :
Two concentric spheres of radii <em>r</em><sub>1</sub> and <em>r</em><sub>2</sub> carry charges <em>q</em><sub>1</sub> and <em>q</em><sub>2</sub> respectively. If the surface charge density (<font face="Symbol">Σ</font>) is the same for both spheres, the electric potential at the common centre will be
Question 9 : In the given figure, find the equivalent capacitance between <em>A</em> and <em>B</em>. <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c2e21da6d070c2abf984"/>
Question 10 : In the circuit shown in figure if switch <em>S</em> is closed, the charge that flows through battery is equal to <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c353bfef6349df00fe9e"/>
Question 11 :
A parallel plate capacitor of capacitance <em>C</em> is charged with a battery of potential <em>V</em>. The battery is then disconnected and electromagnetic waves are incident on negative plate of the capacitor. As a result the negative plate starts emitting electrons towards the positive plate. The current which flows between the plates remains constant till time <em>t</em><sub>1</sub> and then starts decreasing. The potential difference between the plates at time <em>t</em><sub>1</sub> is (Assume plates of capacitor are close to each other)
Question 12 :
The electric potential at a point (<em>x</em>, <em>y</em>) is given by: <em>V</em> = –<em>Kxy</em>. The electric field intensity at a distance <em>r</em> from the origin varies as
Question 13 :
A conducting sphere of radius R is given a charge Q. consider three points B at the surface, A at centre and C at a distance R/2 from the centre. The electric potential at these points are such that
Question 14 :
Let <em>V</em> and <em>E</em> be the potential and the field respectively at a point. Which of the following assertion is correct?
Question 15 :
If there are {tex} n {/tex} capacitors in parallel connected to {tex} V {/tex} volt source, then the energy stored is equal to
Question 16 :
A ball of mass 2 kg having charge 1 <font face="Symbol">µ</font>C is dropped from the top of a high tower. In space electric field exist in horizontal direction away from tower which varies as <em>E</em> = (5−2<em>x</em>) <font face="Symbol">×</font> 10<sup>6</sup> V/m (where <em>x</em>-is horizontal distance from tower), the maximum horizontal distance ball can go from the tower is
Question 17 :
Seven point charges each of charge <em>q</em> is placed at the seven corners of a cube of side <em>a</em> (one corner is empty). Find the magnitude of electric field at centre of cube.
Question 18 :
Two capacitors {tex} \mathrm { C } _ { 1 } {/tex} and {tex} \mathrm { C } _ { 2 } {/tex} are charged to {tex}120 \mathrm { V } {/tex} and {tex}200 \mathrm { V } {/tex} respectively. It is found that connecting them together the potential on each one can be made zero. Then
Question 19 :
A cylinder of radius <em>R</em> and length <em>L</em> is placed in a uniform electric field <em>E</em> parallel to the axis of cylinder. The total flux through the curved surface of the cylinder is given by
Question 20 :
Two identical charges are placed at the two corners of an equilateral triangle. The potential energy of the system is <em>U</em>. The work done in bringing an identical charge from infinity to the third vertex is
Question 21 : As shown in the figure. If value of <em>Q</em>′ is {tex}\frac{Q}{2}{/tex} then what is the value of dielectric constant <em>k</em> is <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c2f44bec8070e4e150d3"/>
Question 22 : Find the work done by the battery of the system as shown in the figure <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c3321da6d070c2abfa22"/>
Question 23 : A charge <em>q</em> is placed at a distance <em>a</em>/2 above the centre of a horizontal square surface of edge <em>a</em> as shown in figure. The electric flux through the square surface is <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c2ed1da6d070c2abf995"/>
Question 24 :
What is the ratio of the electrostatic potentials at one corner and in the centre point of a uniformly charged cube of conductor. (The potential is considered 0 at infinity) -
Question 25 :
A conducting hollow sphere of radius 0.1 m is given a charge of 10 <font face="Symbol">µ</font>C. The electric potential on the surface of sphere will be
Question 26 :
Capacitance of a capacitor becomes {tex}\frac{4}{3}{/tex}times its original value if a dielectric slab of thickness <em>t</em> = <em>d</em>/2 is inserted between the plates (<em>d</em> = separation between the plates). The dielectric constant of the slab is
Question 27 : Four plates of equal area <em>A</em>, are separated by equal distances <em>d</em> and are arranged as shown in the figure. The equivalent capacity between <em>x</em> and <em>y</em> is <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c34ebfef6349df00fe97"/>
Question 28 :
Two point charges {tex} + 8 q {/tex} and {tex} - 2 q {/tex} are located at {tex} x = 0 {/tex} and<br> {tex} x = L {/tex} respectively. The location of a point on the {tex} x {/tex} axis at<br> which the net electric field due to these two point charges is<br> zero is
Question 29 : A capacitor of capacitance ‘<em>C</em>’ is connected with a battery of emf ε as shown. After full charging a dielectric of same size of capacitor and dielectric constant <em>k</em> is inserted then choose correct statements. (capacitor is always connected to battery) <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c2c9bfef6349df00fe39"/>
Question 30 :
A spherical conductor <em>A</em> of radius <em>r</em> is placed concentrically inside a conducting shell <em>B</em> of radius <em>R</em>(<em>R</em> > <em>r</em>). A charge <em>Q</em> is given to <em>A</em>, and then <em>A</em> is joined to <em>B</em> by a metal wire. The charge flowing from <em>A</em> to <em>B</em> will be
Question 31 :
Consider a huge charge reservoir at potential $V=200$ volts. A spherical capacitor $C_{1}=40nF$ is brought in contact with the charge reservoir and then removed. Afterwards, another spherical capacitor $C_{2}=30nF$ is brought in contact with $C_{1}$ and removed. This process is repeated many times . Assume that potential of reservoir does not change during this exercise. Then the charge in $\left ( \mu C \right )$ on $C_{2}$ after a very long time is :<br/>
Question 32 :
If an electron enters into a space between the plates of a parallel plate capacitor at an angle $\alpha$ with the plates and leaves at an angle $\beta$ to the plates. The ratio of it's kinetic energy while entering the capacitor to that leaving will be :<br/>
Question 33 :
A parallel plate capacitor has plates of unequal area. The larger plate is connected to the positive terminal of the battery and the smaller plate to its negative terminal. Let $Q_+$ and $Q_-$ be the charges appearing on the positive and negative plates respectively.
Question 34 :
Two capacitors of capacitance $C_1$ and $C_2$ respectively are charged to $120 V$ and $200 V$ respectively. It is found that by connecting them together the potential on each one can be made zero. Then :<br/>
Question 35 :
Two similar parallel plate capacitors each of capacity $C_o$ are connected in series, The combination is connected with a voltage source of $V_o$. Now separation between the plates of one capacitor is increased by a distance $d$ and the separation between the plates of another capacitor is decreased by the distance $d/2$ The distance between the plates of each capacitor was $d$ before the change in separation. Then, select the correct choice :<br/>
Question 36 :
In 1909, Robert Millikan was the first to find the charge of an electron in his now-famous oil-drop experiment. In that experiment, tiny oil drops were sprayed into a uniform electric field between a horizontal pair of oppositely charged plates.The drops were observed with a magnifying eyepiece, and the electric field was adjusted so that the upward force on some negatively charged oil drops was just sufficient to balance the downward force of gravity. That is, when suspended, upward force qE just equaled mg. Millikan accurately measured the charges on many oil drops and found the values to be whole number multiples of $1.6 \times 10^{-19} C$ the charge of the electron. For this, he won the Nobel prize. Extra electrons on this particular oil drop (given the presently known charge of the electron) are :<br/>
Question 37 :
The space between the plates of a parallel plate capacitor is filled with a 'dielectric' whose 'dielectric constant' varies with distance as per the relation, $K(x)=K_o+\lambda x(\lambda=a$ constant) The capacitance C, of this capacitor, would be related to its 'vacuum' capacitance $C_o$ as per the relation :<br/>
Question 38 : <span class="wysiwyg-font-size-small"><span class="wysiwyg-font-size-small"></span></span><p class="wysiwyg-text-align-left">The plates of a parallel plate capacitor are charged to $200\ V$ and then, the charging battery is disconnected. Now, a dielectric slab of dielectric constant $5$ and thickness $4\ mm$ is inserted between the capacitor plates. To maintain the original capacity, the increase in the separation between the plates of the capacitor is:</p>
Question 39 :
The capacity of a spherical condenser is $1\mu F$. If the spacing between the two spheres is $1\ mm$, the radius of the outer sphere is.
Question 40 :
A capacitor of capacity $10\ \mu F$ is charged to a potential of $10000\ V$ and a wire is stretched by $0.2\ m$ by a force of $5000\ N$. The ration of the potential energies stored in them will be
Question 41 :
A1 $\mu F$ capacitor and a $2\mu F$ capacitor are connected in series across a $1200\ V$ supply line. The charged capacitors are disconnected from the line and from each other and reconnected with terminals of like sign together. Find the final charge on each and the voltage across them :<br/>
Question 42 :
A large insulated sphere of radius $r$ charged with $Q$ units of electricity is placed in contact with a small insulated uncharged sphere of radius $r$' and is then separated. The charge on smaller sphere will now be :<br/>
Question 43 :
Eight mercury drops of equal radius and equal charge combine to form a big drop The capacitance of big drop in comparison the each small drop will be :
Question 44 :
Two spherical conductors $A$ and $B$ or radii $2 mm$ and $3 mm$ are separated by a distance of $5 cm$ and are uniformly charged. If the spheres are connected by a conducting wire, then, in equilibrium position, the ratio of the magnitudes of electric fields at the surface of the spheres $A$ and $B$ is :
Question 45 :
Two identical metal plates are given positive charge ${Q}_{1}$ and ${Q}_{2}$ $\left( <{ Q }_{ 1 } \right)$ respectively. If they are now brought close together to form a parallel plate capacitor with capacitance $C$, the potential difference between them is
Question 46 :
Two metal spheres (radii $r_1, r_2$ with $r_1 < r_2$) are very far apart but are connected by a thin wire. If their combined charge is Q, then what is their common potential?
Question 47 :
If the circumferences of a sphere is $2\ m$, then capacitance of sphere in water would be:
Question 48 :
In 1909, Robert Millikan was the first to find the charge of an electron in his now-famous oil-drop experiment. In that experiment, tiny oil drops were sprayed into a uniform electric field between a horizontal pair of oppositely charged plates.The drops were observed with a magnifying eyepiece, and the electric field was adjusted so that the upward force on some negatively charged oil drops was just sufficient to balance the downward force of gravity. That is, when suspended, upward force qE just equaled mg. Millikan accurately measured the charges on many oil drops and found the values to be whole number multiples of $1.6 \times 10^{-19} C$ the charge of the electron. For this, he won the Nobel prize. If a drop of mass $1.08 \times 10^{-14} kg$ remains stationary in an electric field of $1.68 \times 10^5 NC^{-1}$, then the charge of this drop is :<br/>
Question 49 :
Two point charges $17.7 \mu c$ and $-17,7 \mu c$ separated by a very small distance, are kept inside a large hollow metallic sphere. Electric flux emnating through the sphere is :
Question 50 :
Three capacitors of capacitances 6 µF each are available. The minimum and maximum capacitances, which may be obtained are
Question 51 :
A capacitor is charged and battery is disconnected .Now the distance between the plates is increased slightly
Question 52 :
The capacity of a parallel plate condenser is $C$ . Its capacity when the separation between the plates is halved will be :
Question 53 :
A parallel plate capacitor has an electric field of $105$V /m between the plates .If the charge on one of the capacitor plate is 1$\mu$C,then the magnitude of the force on each capacitor plate is :
Question 54 :
A spherical drop of capacitance $1\ \mu F$ is broken into $8$ drops of equal radius. Then, the capacitance of each small drop is:
Question 55 :
A dielectric slab of thickness $6\ cm$<b> </b>is placed between the plates of a parallel plate capacitor. If the distance between the plates is reduced by $4\ cm$, the capacity of the capacitor remains same. Find the dielectric constant of the medium.
Question 56 :
The magnitude of the electric field $E$ in the annular region of a charged cylindrical capacitor:<br/>
Question 57 :
A capacitance is formed by two identical metal plates. The plates are given charges $Q_1$ and $Q_2 (Q_2 < Q_1) $ . If capacitance of the capacitor is $C,$ what is the p.d. between the plates?
Question 58 :
Two equally charged spheres of radii $a$ and $b$ are connected together. What will be the ratio of electric field intensity on their surfaces?<br/>
Question 59 :
Two plates (area = $5$ ) charged to $ +q_1$ and $+q_2 (q_2 < q_1) $ are brought closer to form a capacitor of capacitance $C$ . The potential difference across the plates is :
Question 60 :
At the moment $t=0$, an electron leaves one plate of a parallel-plate condenser with a negligible velocity. An accelerating voltage varying as $V=at$, where $a$ is a constant is applied between the plates. The separation between the plates is $l$. The velocity of the electron at the moment it reaches the opposite plate will be :<br/>
