Electric Field Due to a Ring Along the Axis

Q.

Electric field vs. distance along the axis is shown for a uniformly charged circular ring

Which of the following represents the complete graph?

1. 

2. 

3. 

4. 

Q.
Uniformly charged ring is shown is figure, $E$ due to ring is maximum at

1. Centre
2. $\infty$
3. $\frac{R}{\sqrt{2}}$ distance from centre
4. $R$ distance from centre

Q. Two concentric rings, one of radius ‘a’ and the other of radius ‘b’, have the charges +q, and $-{\left(\frac{2}{5}\right)}^{\frac{-3}{2}}$ respectively, as shown in the figure. Find the ratio $\frac{b}{a}$ if a charge particle placed on the axis at z = a is in equilibrium.

Q. The magnitude of electric field $E$ in the annular region of a charged cylindrical capacitor

1. varies as $\frac{1}{r}$, where $r$ is the distance from the axis.
2. is higher near the outer cylinder than near to it.
3. is the same throughout.
4. varies as $\frac{1}{r^2}$, where $r$ is the distance from the axis.

Q. A charge of $10\mu C$ is distributed uniformly over the circumference of a ring of radius $3\text{m}$ placed on the $x-y$ plane with the axis at origin. Find electric potential at point $P(0,0,4\text{m})$

1. $1.8\times {10}^6\text{V}$
2. $18\times {10}^4\text{V}$
3. $18\times {10}^3\text{V}$
4. $1.8\times {10}^2\text{V}$