Electric Potential at a Point in Space Due to a Point Charge Q

Q. Ten electrons are equally spaced and fixed around a circle of radius R. Relative to V = 0 at infinity, the electrostatic potential V and the electric field E at the centre C are

1. $V\ne 0$ and $\stackrel{\rightharpoonup }{E}\ne 0$
2. $V\ne 0$ and $\stackrel{\rightharpoonup }{E}=0$
3. $V=0$ and $\stackrel{\rightharpoonup }{E}=0$
4. $V=0$ and $\stackrel{\rightharpoonup }{E}\ne 0$

Q. $n_1$ electrons/sec passes through a given cross-section towards right with a velocity $v_1$ and $n_2$ protons/sec passes through the same cross-section with velocity $v_2$ in the same direction, the current through a given cross-section will be :
$($Given: $n_1=1.5\times {10}^{10},n_2={10}^{10}\text{and charge on electron}=1.6\times {10}^{-19}\text{C})$

1. $4\times {10}^{-9}\text{A}$
2. ${10}^{-9}\text{A}$
3. $8\times {10}^{-10}\text{A}$
4. $0.5\times {10}^{-11}\text{A}$

Q. Two pith balls carrying identical charges are suspended from a common point by strings of equal lengths, the equilibrium separation between them is $r$. Now the strings are rigidly clamped at half the height. The equilibrium separation between the balls now will be :

1. $\frac{r}{2^{1/3}}$
2. $\frac{2r}{3}$
3. $\frac{2r}{\sqrt{3}}$
4. ${\left(\frac{1}{\sqrt{2}}\right)}^2$

Q. A ring of radius $R$ having a linear charge density $\lambda$ moves towards a solid imaginary sphere of radius $\frac{R}{2}$, so that the centre of the ring passes through the centre of sphere. The axis of the ring is perpendicular to the line joining the centres of the ring and the sphere. The maximum flux through the sphere in this process is

1. $\frac{\lambda \pi R}{3{\epsilon }_0}$
2. $\frac{\lambda R}{2{\epsilon }_0}$
3. $\frac{\lambda R}{{\epsilon }_0}$
4. $\frac{\lambda \pi R}{4{\epsilon }_0}$

Q. Four electric charges $+q,+q,-q$ and $-q$ are placed at the corners of a square of side $2L$ (see figure). The electric potential at point $A$ (midway between the two charges $+q$ and $-q$ ) is

1. $\frac{1}{4\pi {\in }_0}\frac{2q}{L}(1+\sqrt{5})$
2. $\frac{1}{4\pi {\in }_0}\frac{2q}{L}(1+\frac{1}{\sqrt{5}})$
3. $\frac{1}{4\pi {\in }_0}\frac{2q}{L}(1-\frac{1}{\sqrt{5}})$
4. Zero

Q. A charge of $5\text{C}$ experiences a force of $5000\text{N}$ when it is kept in a uniform electric field. Find the potential difference (in$\text{V}$) between two points seperated by a distance of $1\text{cm}$.

Q.

An arc of radius r carries charge. The linear density of charge is $\lambda$ and the arc subtends an angle $\frac{\pi }{3}$ at the centre. What is electric potential at the centre?

1. $\frac{\lambda }{4{ϵ}_0}$
2. $\frac{\lambda }{8{ϵ}_0}$
3. $\frac{\lambda }{12{ϵ}_0}$>
4. $\frac{\lambda }{16{ϵ}_0}$

Q. An infinite wire having linear charge density $+\lambda$ is arranged as shown. A charge particle of mass $m$ and charge $q$ is released from point $\text{P}$. Find the initial acceleration of the particle $($at $t=0)$ just after the particle is released.
(Assume the straight parts of wire perpendicular to XY plane.)

1. $\frac{q\lambda }{2\pi {ϵ}_{0}mR}(-\hat{j})$
2. $\frac{2q\lambda }{\pi {ϵ}_{0}mR}\left(\hat{k}\right)$
3. $\frac{q\lambda }{2\pi {ϵ}_{0}mR}\hat{j}$
4. $\frac{q\lambda }{\pi {ϵ}_{0}mR}(-\hat{j})$

Q. Two equal positive charges are fixed along x - axis at $-a$ and $a$ as shown.


$E_x$ and $E_y$ represent electric field along x - and y- axes respectively and $V$ represents potential.

1. A $\to$ R, B $\to$ Q, C $\to$ P, D $\to$ S
2. A $\to$ P, B $\to$ Q, C $\to$ R, D $\to$ S
3. A $\to$ R, B $\to$ S, C $\to$ P, D $\to$ Q
4. A $\to$ R, B $\to$ P, C $\to$ Q, D $\to$ S

Q. Two concentric spheres of radii $R$ and $2R$ are charged. The inner sphere has a charge of $1\mu \text{C}$ and the outer sphere has a charge of $2\mu \text{C}$ of the same sign. The potential is $9000\text{V}$ at a distance $3R$ from the common centre. The value of $R$ is

1. $4\text{m}$
2. $1\text{m}$
3. $2\text{m}$
4. $3\text{m}$

Q. A charge 4C is placed at the origin, what is the electric potential at a point (3, 4, 0)?

1. $\frac{4k}{5}$
2. $\frac{4k}{3}$
3. $\frac{4k}{5}\hat{i}$
4. $\frac{4k}{3}\hat{i}$

Q.

An arc of radius r carries charge. The linear density of charge is $\lambda$ and the arc subtends an angle $\frac{\pi }{3}$ at the centre. What is electric potential at the centre?

1. $\frac{\lambda }{4{ϵ}_0}$
2. $\frac{\lambda }{8{ϵ}_0}$
3. $\frac{\lambda }{12{ϵ}_0}$>
4. $\frac{\lambda }{16{ϵ}_0}$

Q. Two point charges 20mC and - 60 mC are separated by a distance of 16cm. The net electric potential is zero on the line joining them

1. At a distance of 4cm from 20mC in between the charges
2. At a distance of 8cm from 20mC and 24cm from -60 mC
3. Both of the above
4. None of the above

Q. Two electric dipoles, $A$ and $B$ with respective dipole moments ${\overrightarrow{p}}_A=-4qa\hat{i}$ and ${\overrightarrow{p}}_B=-2qa\hat{i}$ are placed on the $X-$ axis with a separation $R$, as shown in the figure


The distance from $A$ at which both of them produce the same potential is

1. $\frac{R}{\sqrt{2}-1}$
2. $\frac{\sqrt{2}R}{\sqrt{2}-1}$
3. $\frac{R}{\sqrt{2}+1}$
4. $\frac{\sqrt{2}R}{\sqrt{2}+1}$

Q. Two charges $4q$ and $q$ are placed $30\text{cm}$ apart. At what point, the value of electric field will be zero?

Q. A charge 4C is placed at the origin, what is the electric potential at a point (3, 4, 0)?

1. $\frac{4k}{5}$
2. $\frac{4k}{3}$
3. $\frac{4k}{5}\hat{i}$
4. $\frac{4k}{3}\hat{i}$

Q. A parallel- plate capacitor is placed in such a way that its plates are horizontal and lower plate is dipped into a liquid of dielectric constant $k$ and density $\rho$. Charge on plates of capacitor is $Q$ and $-Q$. [$+Q$ is charge on upper plate]

1. Level of liquid in the space between plates rises.
2. Level of liquid in the space between plates falls.
3. Net charge on the lower plate is $\frac{-Q}{k}$.
4. Charge induced on the upper surface of liquid is $-Q(1-k)$

Q. Four Charges $1\times {10}^{-8}C,-2\times {10}^{-8}C,3\times {10}^{-8},3\times {10}^{-8}$ are placed at the four corners of a square of side 1 m. The potential at the centre of the square is

1. $450V$
2. $450\sqrt{2}V$
3. $180V$
4. $180\sqrt{2}V$

Q. An infinite number of charges of equal magnitude q, but of opposite sign are placed alternately starting with positive charge along x- axis at x = 1 m; x = 2 m, x = 4 m, x= 8 m and so on. The electric potential at the point x = 0 due to these charges will be (in S.I units and k = $\frac{1}{4\pi {ϵ}_0}$

1. $\frac{kq}{2}$
2. $\frac{kq}{3}$
3. $\frac{k2q}{3}$
4. $\frac{k3q}{2}$

Q. At distance $r$ from a point charge, the ratio $\frac{u}{v^2}$ (where $u$ is energy density and $v$ is potential) is best represented by

1. 
2. 
3. 
4. 

Q. Four Charges $1\times {10}^{-8}C,-2\times {10}^{-8}C,3\times {10}^{-8},3\times {10}^{-8}$ are placed at the four corners of a square of side 1 m. The potential at the centre of the square is

1. $450V$
2. $450\sqrt{2}V$
3. $180V$
4. $180\sqrt{2}V$

Q.

An arc of radius r carries charge. The linear density of charge is $\lambda$ and the arc subtends an angle $\frac{\pi }{3}$ at the centre. What is electric potential at the centre?

1. $\frac{\lambda }{4{ϵ}_0}$
2. $\frac{\lambda }{8{ϵ}_0}$
3. $\frac{\lambda }{12{ϵ}_0}$>
4. $\frac{\lambda }{16{ϵ}_0}$

Q. Two point charges $a$ and $b$ whose magnitudes are same are positioned at a certain distance from each other along the positive $x-$ axis. $a$ is placed at the origin. A graph is plotted between the electric field strength and distance $x$ (measured from $a$). $E$ is taken to be positive if it is along the line joining the two charges from $a$ to $b$. From the graph it can be decided that

1. $a$ is positive, $b$ is negative
2. $a$ is negative, $b$ is positive
3. $a$ and $b$ both are negative
4. $a$ and $b$ both are positive

Q. A charge 4C is placed at the origin. The electric potential at a point (3, 4, 0) is .

1. 4k/5
2. 4k/3
3. 4k/5 $\hat{i}$
4. 4k/3 $\hat{i}$

Q. Two point charges $4\mu C$ and $9\mu C$are separated by a distance of 50 cm. The potential at the point between them where the field has zero strength is

1. $4.5\times {10}^{5}V$
2. $9\times {10}^{5}V$
3. $9\times {10}^{4}V$
4. Zero

Q. A uniformly charged ring has linear charge density $4\frac{C}{m}$. What is the electric potential at its centre?

1. $\frac{\lambda }{{ϵ}_0}$
2. $\frac{5\lambda }{{ϵ}_0}$
3. $\frac{\lambda }{2{ϵ}_0}$
4. $\frac{\lambda }{3{ϵ}_0}$