Equipotential Surfaces

Q.

An infinite line charge produces a field of 9 × 10⁴ N/C at a distance of 2 cm. Calculate the linear charge density.

Q. Two particles of masses m and 2m with charge 2q and 2q are placed in a uniform electric field E and allowed to move for the same time. The ratio of their kinetic energies will be

1. 2 : 1
2. 8 : 1
3. 4 : 1
4. 1 : 4

Q.

Can electric potential be zero when the electric field is not zero?

Q. Equipotential surfaces are shown in the following figure. Then the electric field strength will be

1. $100{\text{Vm}}^{-1}$ along X-axis
2. $100{\text{Vm}}^{-1}$ along Y-axis
3. $200{\text{Vm}}^{-1}$ at an angle ${120}^{\circ }$ with X-axis
4. $50{\text{Vm}}^{-1}$ at an angle ${120}^{\circ }$ with X-axis

Q. Figure shows equipotential concentric surfaces centred at $\text{O}$. The magnitude of electric field at a distance $r$ measured from $\text{O}$ is:

1. $\frac{9}{r^2}{\text{Vm}}^{-1}$
2. $\frac{6}{r^2}{\text{Vm}}^{-1}$
3. $\frac{2}{r^2}{\text{Vm}}^{-1}$
4. $\frac{16}{r^2}{\text{Vm}}^{-1}$

Q.

Show that there can be no net charge in a region in which the electric field uniform at all points.

Q. The diagrams below show regions of equipotentials.

A positive charge $q$ is moved from A to B in each diagram.

1. In all the four cases the work done is the same.
2. Minimum work is required to move $q$ in figure (a).
3. Maximum work is required to move $q$ in figure (b)
4. Maximum work is required to move $q$ in figure (c).

Q. A hollow conducting sphere is placed in an electric field produced by a point charge placed at P as shown in figure. Let $V_A,V_B,V_C$ be the potentials at points A, B and C respectively. Then

1. $V_C>V_B$
2. $V_B>V_C$
3. $V_A>V_B$
4. $V_A=V_C$

Q. A metallic shell has a point charge ‘q’ kept inside its cavity. Which one of the following diagrams correctly represents the electric lines of forces

1. 
2. 
3. 
4. 

Q. The electric field due to a uniformly charged sphere of radius R as a function of the distance from its centre is represented graphically by

1. 
2. 
3. 
4. 

Q. A negatively charged plate has charge density of $2\times {10}^{-6}C/m^2$. The initial distance of an electron which is moving toward plate, cannot strike the plate, if it is having energy of 200 eV

1. 1.77 mm
2. 3.51 mm
3. 1.77 cm
4. 3.51 cm

Q. Which of the following represents the equipotential lines/surfaces of a dipole?

3. D) \( )(( \)

Q. Draw E-r and V - r graphs due to two point charges +q and -2qkept at some distance along the line joining these two charges.

Q. If four identical charged particles of charge q each are kept at vertices of regular pentagon, then force acting on a charge `–q kept at centre of pentagon is (Here, r is distance of vertex from centre of pentagon)

Q. On the $x-$axis at a distance $x$ from the origin, the gravitational field due to a mass distribution is given by $\frac{Ax}{(x^2+a^2{)}^{3/2}}$ in the $x-$direction. The magnitude of gravitational potential on the $x-$ axis at a distance $x$, taking its value to be zero at infinity, is

1. $\frac{A}{(x^2+a^2{)}^{1/2}}$
2. $\frac{A}{(x^2+a^2{)}^{3/2}}$
3. $A(x^2+a^2{)}^{1/2}$
4. $A(x^2+a^2{)}^{3/2}$

Q.

Define electric work.

Q. A uniformly charged solid sphere or radius $R$ has potential $V_0$ (measured with respect to $\infty$) on its surface. For this sphere, the equipotential surfaces with potentials $\frac{3V_0}{2},\frac{{5V}_0}{4},\frac{3V_0}{4},\frac{V_0}{4}$ have radius $R_1,R_2,R_3$ and $R_4$ respectively. Then

1. $R_1=0$ and $R_2<(R_4-R_3)$
2. $R_1\ne 0$ and $(R_1-R_1)>(R_4-R_3)$
3. $R_1=0$ and $R_2>(R_4-R_3)$
4. $2R>R_4$

Q. If a unit positive charge is taken from one point to another over an equipotential surface, then

1. Work is done by the charge
2. Work done is constant
3. No work is done
4. Work is done on the charge

Q. $q_1,q_2,q_3$ and $q_4$ are point charges located at points as shown in the figure and S is a spherical Gaussian surface of radius $R$. Which of the following is true according to the Gauss's law ?

1. $\oint (\overrightarrow{E_1}+\overrightarrow{E_2}+\overrightarrow{E_3}+\overrightarrow{E_4}).\overrightarrow{dA}=\frac{q_1+q_2+q_3+q_4}{{\epsilon }_0}$
2. $\oint (\overrightarrow{E_1}+\overrightarrow{E_2}+\overrightarrow{E_3}+\overrightarrow{E_4}).\overrightarrow{dA}=\frac{q_1+q_2+q_3}{{\epsilon }_0}$
3. $\oint (\overrightarrow{E_1}+\overrightarrow{E_2}+\overrightarrow{E_3}).\overrightarrow{dA}=\frac{q_1+q_2+q_3}{2{\epsilon }_0}$
4. $\oint (\overrightarrow{E_1}+\overrightarrow{E_2}+\overrightarrow{E_3}).\overrightarrow{dA}=q_1+q_2+q_3$

Q.

Can an electric field exist tangential to an equipotential surface?

Q. A point charge $q_0$ is placed at the centre of uniformly charged ring of total charge $Q$ and radius $R$. If the point charge is slightly displaced with negligible force along the axis of the ring then find out its speed when it reaches a large distance $(x>>R)$.

$[\text{Take}K=\frac{1}{4\pi {\epsilon }_0}]$

1. $\sqrt{\frac{KQ{q}_0}{mr}}$

2. $\sqrt{\frac{KQ{q}_0}{2mr}}$

3. $\sqrt{\frac{3KQ{q}_0}{mr}}$

4. $\sqrt{\frac{2KQ{q}_0}{mr}}$

Q.

The dipole moment per unit volume is called__________.

Q. How does the random motion of free electrons in a Conductor gets affected when a potential difference is applied across its ends?

Q. two point charges of +1.0 micro C are kept stationary 2 m apart how much work is needed to be done to bring them 1m apart

Q.

Equipotential surfaces

1. will always be equally spaced.

2. are closer in regions of large electric fields compared to regions of lower electric fields.

3. will be more crowded near regions of large charge densities.

4. will be more crowded near the sharp edges of a conductor.

Q. An uniformly charged thin ring has radius $10\text{cm}$ and total charge $12\text{nC}$. An electron is placed on the ring's axis at a distance $25\text{cm}$ from the centre of the ring and is constrained to stay on the axis of ring. The electron is then released from rest. Find the speed of electron when it reaches the center of the ring.

1. $$20\times {10}^4\text{m/s}$$
2. $$15.45\times {10}^6\text{m/s}$$
3. $$18\times {10}^5\text{m/s}$$
4. $$1.5\times {10}^4\text{m/s}$$

Q. The figure shows the equipotential contours due to three point charges. The labels on the contours are in Volts.

1. The electric field at $e$ is directed normal to the $221.7\text{V}$ contour and away from the $312.1\text{V}$ contour
2. A charge released from rest on one of these contours will not move along the contour
3. Two of charges are positive and one is negative
4. $–118.1\text{J}$ of work is done to move a charge of $1\text{Coulomb}$ from $d$ to $c$ along the contour

Q. Two free point charges +q and +4q are at the co-ordinates (0, 0) and (a, 0). A third charge is placed on the line joining them so that the entire system is in equilibrium. The value and position of the third charge is

1. $-\frac{4q}{9}at(\frac{a}{3},0)$
2. $\frac{2q}{3}at(\frac{a}{3},0)$
3. $-\frac{2q}{3}at(\frac{a}{2},0)$
4. $\frac{4q}{9}at(\frac{2a}{3},0)$

Q. ntWhat minimum work must be done by an external force to bring a charge q=3.00micro coulomb from a great distance away (take r=infinite) to a point 0.500m from a charge Q=20.0micro coulomb?n

Q.

Q. Four identical point charges are placed at the four vertices of a square. The number of null points will be

(What is a null point?)