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Home » Two metal spheres, one of radius and the other of radius respectively have the same surface charge density They are brought in contact and separated. What will be the new surface charge densities on them? (1) (2) (3) (4)
Two metal spheres, one of radius \mathbf{R} and the other of radius 2 R respectively have the same surface charge density \sigma . They are brought in contact and separated. What will be the new surface charge densities on them? (1) \sigma_{1}=\frac{5}{3} \sigma, \sigma_{2}=\frac{5}{6} \sigma (2) \sigma_{1}=\frac{5}{6} \sigma, \sigma_{2}=\frac{5}{2} \sigma (3) \sigma_{1}=\frac{5}{2} \sigma, \sigma_{2}=\frac{5}{6} \sigma (4) \sigma_{1}=\frac{5}{2} \sigma, \sigma_{2}=\frac{5}{3} \sigma
Physics | Physics
Two metal spheres, one of radius \mathbf{R} and the other of radius 2 R respectively have the same surface charge density \sigma . They are brought in contact and separated. What will be the new surface charge densities on them? (1) \sigma_{1}=\frac{5}{3} \sigma, \sigma_{2}=\frac{5}{6} \sigma (2) \sigma_{1}=\frac{5}{6} \sigma, \sigma_{2}=\frac{5}{2} \sigma (3) \sigma_{1}=\frac{5}{2} \sigma, \sigma_{2}=\frac{5}{6} \sigma (4) \sigma_{1}=\frac{5}{2} \sigma, \sigma_{2}=\frac{5}{3} \sigma

Answer (1)
Sol. Q_{1}=\sigma 4 \pi R_{1}{ }^{2}=\sigma 4 \pi R^{2}
\mathbf{Q}_{2}=\sigma 4 \pi(2 R)^{2}=\sigma 16 \pi R^{2}
After Redistribution of charges
\begin{array}{l} \frac{Q_{1}^{\prime}}{Q_{2}^{\prime}}=\frac{R}{2 R} \Rightarrow Q_{2}^{\prime}=2 Q_{1}^{\prime} \\ Q_{1}^{\prime}+Q_{2}^{\prime}=20 a \pi \mathbf{R}^{2} \end{array}
Using eq. (i) and (ii)
\begin{array}{l} Q_{1}^{\prime}=\frac{20}{3} \sigma \pi R^{2} \Rightarrow \sigma_{1}^{\prime}=\frac{5}{3} \sigma \\ Q_{2}^{\prime}=\frac{40}{3} \sigma \pi R^{2} \Rightarrow \sigma_{2}^{\prime}=\frac{5}{6} \sigma \end{array}

i

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