Question

In the electric field due to a point charge $q$, a test charge is carried from $A$ to the points $B$, $C$, $D$ and $E$ lying on the same circle around $q$. The work done is

• A. the least along $AB$
  
• B. the least along $AD$
  
• C. zero along any one of the paths $AB,AD,AC$ and $AE$
  
• D. the least along $AE$.

Answer 1

The correct option is C zero along any one of the paths $AB,AD,AC$ and $AE$

Potential at $A$ due to point charge $=\frac{Kq}{r}$ (radius of sphere $=r$)

$U$ at $B$ $=\frac{Kq}{r}$

work done in moving a test charge from

$A$ to $B$ $=\frac{Kq}{r}-\frac{Kq}{r}$

Similarly for $AD=AC=AE=AB=0$ (Work done)