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Question : 17
Total: 27
Two large charged plane sheets of charge densities σ − 2 σ C ∕ m 2 d
(i) to the left of the first sheet, (ii) to the right of the second sheet, and (iii) between the two sheets.
OR
A spherical conducting shell of inner radiusr 1 r 2 Q
(a) A chargeq
(b) Is the electric field inside a cavity (with no charge) zero-independent of the fact whether the shell is spherical or not? Explain.
(i) to the left of the first sheet, (ii) to the right of the second sheet, and (iii) between the two sheets.
OR
A spherical conducting shell of inner radius
(a) A charge
(b) Is the electric field inside a cavity (with no charge) zero-independent of the fact whether the shell is spherical or not? Explain.
Solution:
Diagram
Deducing electric field expression
(i) To the left of first sheet
(ii) To the right of second sheet
(iii) Between the two sheets
Diagram :
Electric field in the region left of first sheet
E I = E 1 + E 2
E I =
−
E I = +
It is towards right,
Electric field in the region to the right of second sheet
E II =
−
E II = −
It is towards left,
Electric field between the two sheets
E III = E I + E II
E III =
+
E III =
Electric field is towards the right.
OR
Diagram
Finding the surface charge density in the inner and outer surface of the shell
Electric field in the cavity
Diagram:
The surface charge density on inner surface of the shell isσ 1 = −
The surface charge density on outer shell is
σ 2 = −
(b) Consider a Gaussian surface inside the shell, net flux is zero sinceq net = 0
Deducing electric field expression
(i) To the left of first sheet
(ii) To the right of second sheet
(iii) Between the two sheets
Diagram :
Electric field in the region left of first sheet
It is towards right,
Electric field in the region to the right of second sheet
It is towards left,
Electric field between the two sheets
Electric field is towards the right.
OR
Diagram
Finding the surface charge density in the inner and outer surface of the shell
Electric field in the cavity
Diagram:
The surface charge density on inner surface of the shell is
The surface charge density on outer shell is
(b) Consider a Gaussian surface inside the shell, net flux is zero since
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