Question

Three charges are located on a horizontal axis as shown. The potential at a point M at distance r is - (r >> d)

• A. $\frac{kq}{r^{2}}(2d + r)$
• B. $\frac{kq}{r}(2d - r)$
• C. $\frac{kq}{r}(2d + r)$
• D. $\frac{kq}{r^{2}}(d + r)$

Answer 1

Answer: (A)

$\frac{kq}{r^{2}}(2d + r)$

Answer 2

V_M = – $\frac { \mathrm { kq } } { \mathrm { r } + \mathrm { d } } + \frac { \mathrm { kq } } { \mathrm { r } } + \frac { \mathrm { kq } } { \mathrm { r } - \mathrm { d } }$

= kq $\left( \frac { 1 } { \mathrm { r } - \mathrm { d } } - \frac { 1 } { \mathrm { r } + \mathrm { d } } \right) + \frac { \mathrm { kq } } { \mathrm { r } }$

= kq $\frac { \mathrm { kq } 2 \mathrm {~d} } { \mathrm { r } ^ { 2 } } + \frac { \mathrm { kq } } { \mathrm { r } } = \frac { \mathrm { kq } } { \mathrm { r } ^ { 2 } } ( 2 \mathrm {~d} + \mathrm { r } )$