Four points a, b, c and d are set at equal distance from the centre of a dipole as shown in the figure. The magnitudes of electrostatic potential `V_(a), V_(b), V_(c)and V_(d)` would satisfy which of the following relation?

Options

A. `V_(a)gt V_(b) gt V_(c) gt V_(d)`
B. `V_(a) gt V_(b)gt =V_(d)gt V_(c)`
C. `V_(a)=V_(c)gt V_(b)=V_(d)`
D. `V_(b)=V_(d)gt V_(a)gt V_(c)`

Answer

C

Explanation

`V_a` due to `q^+=1/(4piepsilon_0). 1/((x-l))`
`V_a` due to `q^(-)=(-1)/(4piepsilon_0).q/((x+1))`
`therefore V_"a total"=q/(4piepsilon_0).{1/((x-l))-1/((x+l))}`
`V_a=q/(4piepsilon_0). "2l"/((x^2-l^2)) rArr V_a=(2lq)/(4piepsilon_0x^2) " " "(if l lt lt x)" = p/(4piepsilon_0x^2)`
` V_"c"=q/(4piepsilon_0).{1/((x-l))+1/((x+l))}="-2lq"/(4piepsilon_0.(x^2))`
`V_d="+q"/(4piepsilon_0).{1/r-1/r}` due to +q and -q =0
`V_b=0`
`therefore V_a=V_c gt V_b = V_d `