At the centre of a half ring of radius R=10 | vedclass

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

Question

(B) The potential $V$ at the centre of a charged ring is given by $V = \frac{1}{4\pi \epsilon_0} \int \frac{dq}{R}$.For a half ring of radius $R$,the

Vedclass · Accepted Answer

$36$

Vedclass · Answer

(B) The potential $V$ at the centre of a charged ring is given by $V = \frac{1}{4\pi \epsilon_0} \int \frac{dq}{R}$.For a half ring of radius $R$,the total charge $Q = \lambda 	imes (\pi R)$.Since every point on the half ring is at the same distance $R$ from the centre,the potential is $V = \frac{1}{4\pi \epsilon_0} \frac{Q}{R}$.Substituting $Q = \lambda \pi R$,we get $V = \frac{1}{4\pi \epsilon_0} \frac{\lambda \pi R}{R} = \frac{\lambda}{4 \epsilon_0}$.Given $\lambda = 4 	imes 10^{-9} \ C/m$ and $k = \frac{1}{4\pi \epsilon_0} = 9 	imes 10^9 \ N \ m^2/C^2$.$V = k \lambda \pi = (9 	imes 10^9) 	imes (4 	imes 10^{-9}) 	imes \pi$.$V = 36 \pi \ V$.Comparing this with $x \pi \ V$,we find $x = 36$.

At the centre of a half ring of radius $R=10 \ cm$ and linear charge density $\lambda = 4 \ nC \ m^{-1}$,the potential is $x \pi \ V$. The value of $x$ is . . . . .

Similar Questions

An electric charge $10^{-8} \ C$ is placed at the point $(4 \ m, 7 \ m, 2 \ m)$. At the point $(1 \ m, 3 \ m, 2 \ m)$,the electric

$A$ hollow metallic sphere of radius $R$ is given a charge $Q$. Then the potential at the centre is

Along the $x$-axis,three charges $\frac{q}{2}, -q$ and $\frac{q}{2}$ are placed at $x=0, x=a$ and $x=2a$ respectively. The resultant electric potential at a point $P$ located at a distance $r$ from the charge $-q$ $(r > a)$ is ($\varepsilon_0$ is the permittivity of free space):

Two concentric hollow spherical shells have radii $r$ and $R$ $(R \gg r)$. $A$ charge $Q$ is distributed on them such that the surface charge densities are equal. The electric potential at the centre is

What is the change in kinetic energy of an $\alpha$-particle when it moves from a point at $70\ V$ to a point at $50\ V$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module