Question

Quarter non-conducting disc of radius 4R having uniform surface charge density $\sigma$ is placed in xz-plane, then which of the following is correct?

• A. Electric potential at $(0,3R,0)is\frac{\sigma R}{4{ϵ}_0}$
• B. Electric potential at $(0,0,0)\text{is}\frac{\sigma R}{2{ϵ}_0}$
• C. Electric field at (0,3R,0) is symmetric with x and z axis
• D. Electric field intensity at (-4R, 0, -4R) is equally inclined with x and z axis

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A Electric potential at $(0,3R,0)is\frac{\sigma R}{4{ϵ}_0}$
B Electric potential at $(0,0,0)\text{is}\frac{\sigma R}{2{ϵ}_0}$
C Electric field at (0,3R,0) is symmetric with x and z axis
D Electric field intensity at (-4R, 0, -4R) is equally inclined with x and z axis

$\left(A\right)V={\int }_0^{4R}\frac{K\frac{\pi }{2}rdr\sigma }{\sqrt{r^2+(3R{)}^2}}=\frac{\sigma R}{4{ϵ}_0}$
$\left(B\right)V={\int }_0^{4R}\frac{K\frac{\pi }{2}rdr\sigma }{r}=\frac{\sigma R}{2{ϵ}_0}$
(C) Given point is symmetric w.r.t x-axis and z-axis.
(D) Given point is symmetric w.r.t x-axis and z-axis.