Question: An expanding sphere, radius R(t) = vt (t > 0, constant v) carries a charge Q, uniformly distributed over its volume. Evaluate the integral Q

An expanding sphere, radius R(t) = vt (t > 0, constant v) carries a charge Q, uniformly distributed over its volume. Evaluate the integral Q_eff =ρ(r, tr) dτ with respect to the center. Show that Q_eff ≈ Q(1 − 3v/4c ), if v << c.

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