Question

Charges are placed on the vertices of a square as shown. Let $\overset{\rightarrow}{E}$ be the electric field and V the potential at the centre. If the charges on A and B are interchanged with those on D and C respectively, then–

• A. $\overset{\rightarrow}{E}$remains unchanged, V changes
• B. Both $\overset{\rightarrow}{E}$ and V changes
• C. $\overset{\rightarrow}{E}$and V remains unchanged
• D. $\overset{\rightarrow}{E}$changes, V remains unchanged

Answer 1

Answer: (D)

$\overset{\rightarrow}{E}$changes, V remains unchanged

Answer 2

V₀ = $\frac { \mathrm { kq } } { \mathrm { r } }$ + $\frac { \mathrm { kq } } { \mathrm { r } }$ –$\frac { \mathrm { kq } } { \mathrm { r } }$–$\frac { \mathrm { kq } } { \mathrm { r } }$= 0

E_R = 2 (2E) cos 45 = 2$\sqrt { 2 }$ $\frac { \mathrm { kq } } { \mathrm { r } ^ { 2 } }$ –

After interchanging

V₀ = $\frac { \mathrm { kq } } { \mathrm { r } }$ + $\frac { \mathrm { kq } } { \mathrm { r } }$ –$\frac { \mathrm { kq } } { \mathrm { r } }$–$\frac { \mathrm { kq } } { \mathrm { r } }$= 0

E_R = 2$\sqrt { 2 }$ $\frac { \mathrm { kq } } { \mathrm { r } ^ { 2 } }$ $\hat { \mathrm { j } }$

Hence Electric field will change.