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Q.

Consider a uniform charge distribution with charge density 2 C/m3 throughout in space. If a Gaussian sphere has a variable radius which changes at the rate of 2 m/s, then value of rate of charge of flux is proportional to rk, (r= radius of sphere). Then, the value of k is _____________.

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answer is 2.

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Detailed Solution

Flux linked with a Gaussian sphere of radius r= change enclosed ×1ε0= volume enclosed × charge density ×1ε0=43πr3×ρ×1ε0 So, rate of change of flux =dϕEdt=ddt43πρε0×r3=43πρε0×3r2drdt=4πr2ρε0drdt=8πr2ρε0∴ dϕEdt∝r2,k=2
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