JEE Main · 2020 · 07 Jan 2020 · Shift 1 · Electrostatics

Two infinite planes each with uniform surface charge density

+ σ

are kept in such a way that the angle between them is

3 0^{\circ}

. The electric field in the region shown between them is given by:

(A) $\frac{σ}{2 ε _{0}} [(1 - \frac{3}{2}) \overset{y}{^} - \frac{x ^}{2}]$ ✓ Correct
(B) $\frac{σ}{2 ε _{0}} [(1 + 3) \overset{y}{^} - \frac{x ^}{2}]$
(C) $\frac{σ}{2 ε _{0}} [(1 + 3) \overset{y}{^} + \frac{x ^}{2}]$
(D) $\frac{σ}{ε _{0}} [(1 + \frac{3}{2}) \overset{y}{^} + \frac{x ^}{2}]$

Answer: (A)

Solution

Each infinite sheet produces a uniform field of magnitude

\frac{σ}{2 ε _{0}}

directed away from it. The horizontal sheet contributes

\frac{σ}{2 ε _{0}} \overset{y}{^}

, while the sheet inclined at

3 0^{\circ}

contributes

- \frac{σ}{2 ε _{0}} cos 6 0^{\circ} \overset{x}{^} - \frac{σ}{2 ε _{0}} sin 6 0^{\circ} \overset{y}{^}

once its normal is resolved. Adding the two fields in the region between the planes gives

E = \frac{σ}{2 ε _{0}} [(1 - \frac{3}{2}) \overset{y}{^} - \frac{1}{2} \overset{x}{^}]

JEE Main · 2020 · 07 Jan 2020 · Shift 1 · Single correct option