Question

Two point charges $+q$ and $-q$ are held fixed at $(-d,0)$ and $(d,0)$ respectively of a $(x,y)$ coordinate system, then

• A. the electric field $\overrightarrow{E}$ at all points on the x-axis has the same direction
• B. $\overrightarrow{E}$ at all points on the y-axis is along $\hat{i}$
• C. positive work is done in bringing a test charge from infinity to the origin
• D. all of the above

Answer 1

The correct option is B $\overrightarrow{E}$ at all points on the y-axis is along $\hat{i}$

Here the electric field is non zero between the two charges i.e., between $(-a,0)and(a,0)$.

So option A is incorrect.

The vector sum of electric field at point of y-axis is along x-axis itself. so option B is correct.

At origin potential is $kq/a+k(-q)/a=0$ at infinity, potential is $0$.

So work done to bring +ve charge from infinity to origin is zero.

So option C is incorrect.