A charged spherical conductor has radius 'r'. | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The potential at the surface of the conductor is $V_s = \frac{q}{4\pi\varepsilon_0 r}$.The potential at a distance $3r$ from the center is $V_p =

Vedclass · Accepted Answer

$\frac{V}{6r}$

Vedclass · Answer

(D) The potential at the surface of the conductor is $V_s = \frac{q}{4\pi\varepsilon_0 r}$.The potential at a distance $3r$ from the center is $V_p = \frac{q}{4\pi\varepsilon_0 (3r)}$.The potential difference $V$ is given by $V = V_s - V_p = \frac{q}{4\pi\varepsilon_0 r} - \frac{q}{12\pi\varepsilon_0 r} = \frac{q}{4\pi\varepsilon_0 r} \left(1 - \frac{1}{3}\right) = \frac{2q}{12\pi\varepsilon_0 r} = \frac{q}{6\pi\varepsilon_0 r}$.Thus,$\frac{q}{4\pi\varepsilon_0} = \frac{3}{2} Vr$.The electric intensity $E$ at a distance $3r$ is $E = \frac{q}{4\pi\varepsilon_0 (3r)^2} = \frac{q}{4\pi\varepsilon_0 (9r^2)}$.Substituting the value of $\frac{q}{4\pi\varepsilon_0}$,we get $E = \frac{3Vr}{2(9r^2)} = \frac{V}{6r}$.

$A$ charged spherical conductor has radius '$r$'. The potential difference between its surface and a point at a distance '$3r$' from the center is '$V$'. The electric intensity at a distance '$3r$' from the center of the conductor is:

Similar Questions

$A$ proton is $1840$ times heavier than an electron. When it is accelerated through a potential difference of $1 \ kV$,its kinetic energy is .......... $keV$.

$A$ hollow metal sphere is charged with a charge of $3.2 \times 10^{-19} \ C$. If the radius of the sphere is $10 \ cm$,then the electric potential at a distance of $4 \ cm$ from its center will be:

The potential of a large liquid drop formed when eight identical small liquid drops are combined is $20 \,V$. What was the potential of each single small drop (in $\,V$)?

Two identical positive charges are placed on the $y$-axis at $y=-a$ and $y=+a$. The variation of $V$ (electric potential) along the $x$-axis is shown by which graph?

Electric charges of $+10\,\mu C, +5\,\mu C, -3\,\mu C$ and $+8\,\mu C$ are placed at the corners of a square of side $\sqrt{2}\,m$. The potential at the centre of the square is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module