Question

X and Y are large, parallel conducting plate close to each other. Each face has an Area A, X is given a charge Q, Y is without any charge. Points A, B and C are as shown in figure.

• A. The field at B is $d\frac{Q}{2{\epsilon }_{0}A}$
• B. The field at B is $\frac{Q}{{\epsilon }_{0}A}$
• C. The field at A, B and C are of the same magnitude
• D. The field at A and C are of the same magnitude, but in opposite directions

Answer 1

Answer: (B), (D)

The correct options are
B The field at B is $\frac{Q}{{\epsilon }_{0}A}$
D The field at A and C are of the same magnitude, but in opposite directions

The field at $A$ due to plate $X=\frac{q}{2{\epsilon }_{o}A}$(toward left)

The field at $A$ due to the plate $Y=0$

so, total field at $A=E_X+E_Y$

$=\frac{q}{{\epsilon }_{o}A}$ (towards left)

Similarly,

Total field at $B=E_Z+E_Y$

$=\frac{q}{{\epsilon }_{o}A}$ (towards right)

Total field at $C=E_X+E_Y$

$=\frac{q}{{\epsilon }_{o}A}$ (Toward Right)