Assertion: For a non-uniformly charged thin c | vedclass

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

Question

(D) For a thin circular ring with a non-uniform charge distribution and a net charge of $0$,the electric potential $V$ at any point $P$ on the axis is

Vedclass · Accepted Answer

If Assertion is incorrect but Reason is correct.

Vedclass · Answer

(D) For a thin circular ring with a non-uniform charge distribution and a net charge of $0$,the electric potential $V$ at any point $P$ on the axis is given by $V = \frac{1}{4\pi\epsilon_0} \int \frac{dq}{r}$. Since the net charge $\int dq = 0$ and all points on the ring are at the same distance $r$ from any point on the axis,the potential $V$ is indeed $0$ at every point on the axis.However,the electric field $\vec{E}$ is the negative gradient of the potential,$\vec{E} = -
abla V$. While the potential is zero everywhere on the axis,it does not mean the potential is constant in the neighborhood of the axis. In fact,the electric field on the axis is generally non-zero and directed perpendicular to the axis. Thus,the Assertion is incorrect,and the Reason is correct.

Assertion: For a non-uniformly charged thin circular ring with net charge $0$,the electric field at any point on the axis of the ring is zero.
Reason: For a non-uniformly charged thin circular ring with net charge $0$,the electric potential at each point on the axis of the ring is zero.

Similar Questions

Why is an electric force conservative?

Two point charges $q_1 = \sqrt{10} \, \mu C$ and $q_2 = -25 \, \mu C$ are placed on the $x$-axis at $x = 1 \, m$ and $x = 4 \, m$ respectively. The electric field (in $V/m$) at a point $y = 3 \, m$ on the $y$-axis is,[ take $\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9 \, Nm^2C^{-2}$ ]

Two point charges of magnitudes $-8 \mu C$ and $+32 \mu C$ are separated by a distance of $15 \ cm$ in air. The position of the point from the $-8 \mu C$ charge at which the resultant electric field becomes zero is (in $cm$)

Four equal charges of value $+Q$ are placed at four vertices of a regular hexagon of side $a$. By suitably choosing the vertices, what can be the maximum possible magnitude of the electric field at the centre of the hexagon?

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Assertion: For a non-uniformly charged thin circular ring with net charge $0$,the electric field at any point on the axis of the ring is zero.Reason: For a non-uniformly charged thin circular ring with net charge $0$,the electric potential at each point on the axis of the ring is zero.