Question

A wire having a uniform linear charge density $\lambda$, is bent in the form of a ring of radius R. Point A as shown in the figure, is in the plane of the right but not at the centre, two elements of the ring of lenghts $a_1$ and $a_2$ subtend very same angle at the point A. They are at a distances $r_1$ and $r_2$ from the point A respectively:

• A. The ratio of charge of elements $a_1$ and $a_2$ is $\frac{r_1}{r_2}$
• B. The element $a_1$ produced greater magnitude of electric field at A than element $a_2$
• C. The elements $a_1$ and $a_2$ produce same potential at A
• D. The direction of net electric field at A is towards element $a_2$

Answer 1

Answer: (A), (C)

The correct options are
A The ratio of charge of elements $a_1$ and $a_2$ is $\frac{r_1}{r_2}$
C The elements $a_1$ and $a_2$ produce same potential at A

Charge on $a_1=\left(r_1\theta \right)\lambda$; Charge on $a_2=\left(r_2\theta \right)\lambda$
Ratio of charges $=\frac{r_1}{r_2}$.
Potential from $a_1=\left(k\right(r_1\theta \left)\lambda \right)/r_1=k\theta \lambda$
Potential from $a_2=\left(k\right(r_2\theta \left)\lambda \right)/r_2=k\theta \lambda$