An arc of radius r carries charge. The linear density of charge is λ and the arc subtends a angle π3 at the centre. What is electric potential at the centre ?

Length of the arc, s=rθ=πr3Charge on the arc, q=πr3×λPotential at center, V=kqr=14πε0×πr3×λr=λ12ε0

An arc of radius r carries charge. The linear density of charge is λ and the arc subtends a angle π3 at the centre. What is electric potential at the centre ?

Length of the arc, s=rθ=πr3Charge on the arc, q=πr3×λPotential at center, V=kqr=14πε0×πr3×λr=λ12ε0

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An arc of radius r carries charge. The linear density of charge is $λ$ and the arc subtends a angle $\frac{π}{3}$ at the centre. What is electric potential at the centre ?

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$\frac{λ}{8 ε_{0}}$

$\frac{λ}{12 ε_{0}}$

$\frac{λ}{16 ε_{0}}$

$\frac{λ}{4 ε_{0}}$

answer is C.

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Detailed Solution

Length of the arc, $s = rθ = \frac{πr}{3}$

Charge on the arc, $q = \frac{πr}{3} \times λ$

Potential at center, $V = \frac{kq}{r} = \frac{1}{4 {πε}_{0}} \times \frac{πr}{3} \times \frac{λ}{r} = \frac{λ}{12 ε_{0}}$

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An arc of radius r carries charge. The linear density of charge is λ and the arc subtends a angle π3 at the centre. What is electric potential at the centre ?

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An arc of radius r carries charge. The linear density of charge is $λ$ and the arc subtends a angle $\frac{π}{3}$ at the centre. What is electric potential at the centre ?