Visualising Potential

Q. Two concentric conducting spheres are of radii $r_1$ and $r_2$. The outer sphere is given a charge $q$. The charge $q^{\prime }$ on the inner sphere will be (inner sphere is grounded) :-

1. $q$
2. $-q$
3. $-q\frac{r_1}{r_2}$
4. Zero

Q. A solid conducting sphere of radius ${}^{\prime }{a}^{\prime }$ is surrounded by a thin uncharged concentric conducting shell of radius $2a$. A point charge $q$ is placed at a distance $4a$ from common centre of conducting sphere and shell. The inner sphere is then grounded .The charge on the solid sphere is $\frac{-q}{n}$. Find the value of $n$

Q. Two thin conducting shells of radii $R$ and $3R$ are shown in the figure. The outer shell carries a charge $+Q$ and the inner shell is neutral. The inner shell is earthed with the help of a switch $S$.

1. With the switch $S$ open, the potential of the inner sphere is equal to that of the outer
2. When the switch $S$ is closed, the potential of the inner sphere becomes zero
3. With the switch $S$ closed, the charge attained by the inner sphere is $-1/3$ times that of charge present on the outer sphere.
4. By closing the switch the capacitance of the system increases

Q. A concentric spherical cavity is cut out from a solid conducting sphere and a charge $+Q$ is placed at the centre of the cavity. The magnitude of net electric field $E$ and net potential $V$ at point $A$ is

1. $E=0,V=0$
2. $E=0,V=\frac{kQ}{2R}$
3. $E=\frac{kQ}{R^2},V=\frac{kQ}{2R}$
4. $E=0,V=\frac{3kQ}{2R}$

Q. A spherical metal shell $A$ of radius $R_A$ and a solid metal sphere $B$ of radius $R_B(<R_A)$ are kept far apart and each is given charge $Q.$ Now they are connected by a thin metal wire.
Then

1. ${\left(E_A\right)}_{\text{inside}}=0$
2. $Q_A>Q_B$
3. $\frac{{\sigma }_A}{{\sigma }_B}=\frac{R_B}{R_A}$
4. $\frac{{\sigma }_A}{{\sigma }_B}=\frac{R_A}{R_B}$

Q. Three concentric conducting spherical shell have radii $r,2r$ and $3r$ and charges $q_1,q_2,\text{and}{q}_3$ respectively. Innermost and outermost shells are earthed as shown n figure. Select the correct alternative(s).

1. $q_1+q_3=-q_2$
2. $q_1=-\frac{q_2}{4}$
3. $\frac{q_3}{q_1}=3$
4. $\frac{q_3}{q_2}=-\frac{1}{3}$

Q. The figure shows a spherical capacitor with inner sphere earthed. If $a=2\text{cm}$ and $b=3\text{cm}$, then the capacitance of the system is
(Take $k=9\times {10}^9{\text{Nm}}^2/{\text{C}}^2$)

1. $5\text{pF}$
2. $10\text{pF}$
3. $40\text{pF}$
4. $20\text{pF}$

Q. Two concentric spherical shells have charges $+q$ and $-q$ as shown in the figure. Choose the correct options.

1. At $\text{A}$ electric field is zero, but electric potential is non- zero
2. At $\text{B}$ electric field and electric potential both are non-zero.
3. At $\text{C}$ electric field is zero but electric potential is non- zero.
4. At $\text{C}$ electric field and electric potential both are zero.

Q. Two concentric conducting spheres of radii $R$ and $2R$ are carrying charges $Q$ and $-2Q$ respectively. If the charge on inner sphere is doubled, the potential difference between the two spheres will

1. become two times
2. become four times
3. be halved
4. remain same

Q. The figure shows spherical conducting shells with inner sphere earthed. If $a=8\text{cm}$ and $b=9\text{cm}$, then the capacitance of the system is (in $\text{pF}$)

Q. A spherical capacitor consists of an inner sphere of radius $12\text{cm}$ and the outer sphere of radius $36\text{cm}$. The capacitance is $C_1$ when the inner sphere is charged and the outer sphere is earthed and $C_2$ when the inner sphere is earthed and outer sphere is charged. The ratio $\frac{C_1}{C_2}$ is

1. $3$
2. $\frac{1}{3}$
3. $\frac{1}{6}$
4. $\frac{1}{9}$

Q. A hollow conducting spherical shell of inner radius $R_1$ and outer radius $R_2$ encloses a charge $q$ inside, which is located at a distance $d,(d<R_1$) from the centre of the sphere. (assume potential to be zero at infinity) :-

1. The potential at the centre of the shell is $\frac{kq}{d}-\frac{kq}{R_1}$
2. The potential of the shell is $\frac{kq}{R_2}$
3. The potential outside the shell at a distance R from the centre is$\frac{kq}{R}+\frac{kq}{d}-\frac{kq}{R_1}$
4. The potential at the centre of the shell is $\frac{kq}{d}-\frac{kq}{R_1}+\frac{kq}{R_2}$

Q. Two concentric spherical conducting shells of radii $R$ and $2R$ carry charges $Q$ and $2Q$ respectively. Change in electric potential on the outer shell when both are connected by a conducting wire is:
(Where $K=\frac{1}{4\pi {ϵ}_0}$)

1. Zero
2. $\frac{3KQ}{2R}$
3. $\frac{KQ}{R}$
4. $\frac{2KQ}{R}$

Q. A solid conducting sphere of radius $a$ is surrounded by a thin uncharged concentric conducting shell of radius $2a$. A point charge $q$ is placed at a distance $4a$ from common centre of conducting sphere and shell. The inner sphere is then grounded.


The potential of outer shell is:

1. $\frac{q}{32\pi {ϵ}_{0}a}$
2. $\frac{q}{16\pi {ϵ}_{0}a}$
3. $\frac{q}{8\pi {ϵ}_{0}a}$
4. $\frac{q}{4\pi {ϵ}_{0}a}$

Q. A spherical metal shell of radius $R_A$ and a solid metal sphere of radius $R_B$ $(<R_A)$ are kept far apart and each is given a charge $+\text{Q}$. Then they are connected by a thin wire. Choose the correct option.

1. The electric field inside the shell is zero.
2. Charge on metal shell is greater than charge on solid metal.
3. $\frac{\text{Surface charge density of shell}}{\text{Surface charge density of solid sphere}}=\frac{R_B}{R_A}$
4. All of the above

Q. A spherical capacitor consists of two concentric spherical conductors, held in position by suitable insulating supports (Fig.). Show that the capacitance of a spherical capacitor is given by
$c=\frac{4\pi {ϵ}_0{r}_1{r}_2}{r_1-r_2}$
where $r_1$ and $r_2$ are the radii of outer and inner spheres, respectively.

Q. Three point charges of $+2q$, $+2q$ and $-4q$ are placed at the corners $A$, $B$ and $C$ of an equilateral triangle $ABC$ of side '$x$'. The magnitude of the electric dipole moment of this system is :

1. $2qx$
2. $3\sqrt{2}qx$
3. $3qx$
4. $2\sqrt{3}qx$

Q. The figure shows spherical conducting shells with inner sphere earthed. If $a=2\text{cm}$ and $b=3\text{cm}$, then the capacitance of the system is

1. $40\text{pF}$
   
2. $20\text{pF}$
3. $5\text{pF}$
4. $10\text{pF}$

Q. Figure shows two conducting thin concentric shells of radii $r$ and $3r$. The outer shell carries a charge $q$ and the inner shell is neutral. The charge that will flow from inner shell to earth after the switch $S$ is closed is

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

Q. A spherical conductor of radius $4\text{cm}$ carries a charge of $1.11\times {10}^{–10}\text{C}$. At what distance (in $\text{cm}$) from the centre of sphere should a point charge of $4.44\times {10}^{–10}\text{C}$ be placed so that the potential of the conductor becomes $50\text{V}?$ (integer only)
[Assume $V=0\text{at}\infty$]

Q. A long cylinder contains uniformly distributed charge density $\rho$. The electric field at a point $P$ inside the cylinder at a distance $x$ from the axis is :

1. $\frac{\rho x}{2{\epsilon }_0}$
2. $\frac{\rho x}{3{\epsilon }_0}$
3. $\frac{\rho x}{4{\epsilon }_0}$
4. none of these

Q. Figure shows three concentric thin spherical shells $A,B$ and $C$ of radii $R,2R$ and $3R$. The shell $B$ is earthed and $A$ and $C$ are given charges $q$ and $2q$ respectively. Find the charges appearing on the outer surface of $C$.

1. $-\frac{4}{3}q$
2. $\frac{4}{3}q$
3. $\frac{2}{3}q$
4. $q$

Q. The figure shows spherical conducting shells with inner sphere earthed. If $a=8\text{cm}$ and $b=9\text{cm}$, then the capacitance of the system is

1. $10\text{pF}$
2. $9\text{pF}$
3. $100\text{pF}$
4. $90\text{pF}$

Q. A solid conducting sphere of radius $a$ is surrounded by a thin uncharged concentric conducting shell of radius $2a$. A point charge $q$ is placed at a distance $4a$ from common centre of conducting sphere and shell. The inner sphere is then grounded. The charge on solid sphere is

1. $-\frac{q}{2}$
2. $-\frac{q}{4}$
3. $-\frac{q}{8}$
4. $-\frac{q}{16}$

Q. Two particles A and B, having opposite charges $2.0\times {10}^{-6}$C and $-2.0\times {10}^{-6}$C, are placed at a separation of $1.0$cm. Calculate the electric field at a point on th axis of the dipole $1.0$cm away from the centre.

Q. What is the electric field intensity at a point at distance $20cm$ on a line making an angle of ${45}^o$ with the axis of the dipole of moment $10C-m$?

1. $1.77\times {10}^{13}$ $V/m$
2. $0.177\times {10}^{13}$ $V/m$
3. $17.7\times {10}^{13}$ $V/m$
4. $177\times {10}^{13}$ $V/m$

Q. Figure shows a system of three concentric metal shells $\text{A, B}$ and $\text{C}$ with radii $a,2a$ and $3a$ respectively. Shell $\text{B}$ is earthed and shell$\text{C}$ is given a charge $Q$. Now, if shell $\text{C}$ is connected to shell $\text{A}$, then the final charge on the shell $\text{B}$ is equal to

1. $-\frac{4Q}{13}$
2. $-\frac{8Q}{11}$
3. $-\frac{5Q}{3}$
4. $-\frac{3Q}{7}$

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

Q. A solid conducting sphere of radius ${}^{\prime }{a}^{\prime }$ is surrounded by a thin uncharged concentric conducting shell of radius $2a$ $A$ point charge $q$ is placed at a distance $4a$ from common centre of conducting sphere and shell.The inner sphere is then grounded.The potential of outer shell is found to be
$\frac{q}{n\pi {\epsilon }_{0}a}$

Q. A conducting sphere of radius $10cm$ has a charge $30\mu C$. When this sphere is put in contact with other uncharge conducting sphere of radius $20cm$, then find the value of charge on both the sphere