Question

Two nonconducting infinite planes sheets having charges Q and 2Q are placed parallel to each other as shown in figure. The charge distribution on the four faces of the two plates is also shown. The electric field intensities at three points 1, 2, and 3 are `vecE_1, vecE_2, and vecE_3`, respectively. Then the magnitudes of `vecE_1 , vecE_2, and vecE_3` are, respectively (surface area of plates ) :

A. `zero, Q/(epsilon_0S),zero`
B. `(5Q)/(6epsilon_0S), Q/(2epsilon_0S),zero`
C. `(5Q)/(6epsilon_0S), Q/(2epsilon_0S),Q/(3epsilon_0S)`
D. `zero, Q/(2epsilon_0S),zero`

Answer 1

Correct Answer - B
Let us take rightward as positive and leftward as negative.
These four faces can be considered four thin infinite plane sheets.
`vecE_1 = 1/(2epsilon_0S) [ (2Q)/3 - Q/3 - Q/2 - (3Q)/2] = (-5Q)/(6epsilon_0S)`
`vecE_2 = 1/(2epsilon_0S) [ (2Q)/3 + Q/3 - Q/2 - (3Q)/2] = (-Q)/(2epsilon_0S)`
`vecE_3 = 1/(2epsilon_0S) [ (2Q)/3 + Q/3 + Q/2 - (3Q)/2] =0`