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  • Find the equation of the equipotential for an infinite cylinder of radius r_{0}, carrying charge of linear density lambda.

Find the equation of the equipotential for an infinite cylinder of radius r_{0}, carrying charge of linear density \lambda.

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Explanation:-

We have an infinitely long, uniformly charged cylinder of radius R, with a linear charge density λ (charge per unit length). The electric field outside an infinitely long, uniformly charged cylinder (for r>R) is radially symmetric, depending only on the distance from the axis of the cylinder.

An equipotential surface is a surface where the potential is constant. For an infinite cylinder, the potential depends only on the radial distance r, meaning that the potential is constant at any given distance from the axis of the cylinder. We know, the equation of the equipotential for an infinite cylinder of radius r_{0} with linear charge density \lambda is:

r=r_{0}e^{-2\pi \varepsilon _{0} \left [ V(r)-V(r_{0}) \right ]/\lambda}

 

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