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A semicircular non conducting ring of radius R is uniformly charged with total charge Q. find the electrostatic force on q placed at the centre of curvature of half ring

A semicircular non conducting ring of radius R is uniformly charged with total charge Q. find the electrostatic force on q placed at the centre of curvature of half ring

Grade:12th pass

1 Answers

Eshan
askIITians Faculty 2095 Points
5 years ago
Dear student,

The charge per unit length of the ring=\lambda=\dfrac{Q}{\pi R}
Electric field at the center of curvature of half ring=E=\int_{-\pi/2}^{\pi/2}\dfrac{k(\lambda Rd\theta)}{R^2}cos\theta
=\dfrac{2k\lambda }{R}=\dfrac{\lambda}{2\pi\epsilon_0 R}

Hence force on the charge kept at that point=qE=\dfrac{\lambda q}{2\pi\epsilon_0R}=\dfrac{Qq}{2\pi^2\epsilon_0 R^2}

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