A uniformly charged solid sphere of radius R has potential V0 (measured with respect to ) on its surface. For this sphere the equipotential surfaces with potentials have radius R1, R2, R3 and R4 respectively. Then

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Physics

Electric Potential Energy and Electric Potential

Question

A uniformly charged solid sphere of radius R has potential V₀ (measured with respect to $\infty$ ) on its surface. For this sphere the equipotential surfaces with potentials $\frac{3 V_{0}}{2}, \frac{5 V_{0}}{4}, \frac{3 V_{0}}{4} and \frac{V_{0}}{4}$ have radius R₁, R₂, R₃ and R₄ respectively. Then

2R < R₄

R₁ $\neq$ 0 and (R₂ – R₁) > (R₄ – R₃)

R₁ = 0 and R₂ < (R₄ – R₃)

R₁ = 0 and R₂ > (R₄ – R₃)

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$V_{0} = \frac{kQ}{R}$

$V_{centre} = \frac{3 kQ}{2 R} = \frac{3 V_{0}}{2}$

⇒ R₁ = 0

$\frac{5 kQ}{4 R} = \frac{kQ}{2 R^{3}} (3 R^{2} - x^{2})$

$R_{2} = \frac{R}{\sqrt{2}}$

$R_{3} = \frac{4 R}{3}$

R₄ = 4R

$\frac{R}{\sqrt{2}} < \frac{8 R}{3} & 2 R < 4 R$