GATE EC 2016 Set 1 — Question 34
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Electromagnetics → Maxwell's Equations → Differential & Integral Forms
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Question
Concentric spherical shells of radii 2 m, 4 m, and 8 m carry uniform surface charge densities of 20 nC/m, -4 nC/m and , respectively. The value of (nC/m) required to ensure that the electric flux density at radius 10 m is ________.
Correct answer
-0.28
Solution
According to Gauss's Law, the electric flux density at a radius from the center of a spherically symmetric charge distribution is given by:
where is the total charge enclosed within a spherical Gaussian surface of radius .We are given three concentric spherical shells:
At m, the Gaussian surface encloses all three shells. Therefore, the total enclosed charge must be the sum of the charges on all three shells.
nCFor at m, the total enclosed charge must be zero.
nC/m.Thus, the value of required is -0.25 nC/m.
where is the total charge enclosed within a spherical Gaussian surface of radius .We are given three concentric spherical shells:
1.Shell 1: Radius m, surface charge density nC/m.
Charge nC.2.Shell 2: Radius m, surface charge density nC/m.
Charge nC.3.Shell 3: Radius m, surface charge density nC/m.
Charge nC.We need the electric flux density at a radius m.At m, the Gaussian surface encloses all three shells. Therefore, the total enclosed charge must be the sum of the charges on all three shells.
nCFor at m, the total enclosed charge must be zero.
nC/m.Thus, the value of required is -0.25 nC/m.
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