Two infinite , parallel, nonconducting sheets carry equal positive charge density $σ$ one is placed in the yz plane at x=0 and the other at distance x = a. Take potential V = 0 at x = 0. Then

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$for 0 \leq x \leq a, potential V = 0$

$for x \geq a, potential V = \frac{σ}{ε_{0}} (x - a)$

$for x \geq a, potential V = - \frac{σ}{ε_{0}} (x - a)$

$for x \leq 0, potential V = \frac{σ}{ε_{0}} x$

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$\begin{array}{l} 0 < x < a \\ V_{x} = [- \int_{0}^{x} E_{x} d x] + V_{0} = 0 (a s E_{x} = 0) \\ x \geq a, V_{x} = - \int_{a}^{x} E_{x} d x + V_{(a)} \\ V_{x} = [- \int_{a}^{x} \frac{σ}{ε_{0}} d x] + V_{(a)} = - \frac{σ}{ε_{0}} (x - a) \\ x \leq a, V_{x} = - \int_{0}^{x} E_{x} d x + V_{(0)} \\ [∴ E_{x} = - \frac{σ}{ε_{0}}] \\ V_{(x)} = - (\frac{- σ}{ε_{0}} x) + V_{(0)} = \frac{σ}{ε_{0}} x \end{array}$