Question

A spherical shell has one half uniformly charged positive, while the other half is uniformly charged with an equal amount of negative charge. What is the electric field at the center?

Answer 1

Answer:

Electric field at the center of the shell is given as

$E = \frac{\sigma}{2\epsilon_0}$

Explanation:

Electric field due to uniformly charged spherical shell is given as

$E = \int \frac{kdq x}{R^3}$

here we know that

$dq = \sigma 2\pi (Rsin\theta)(Rd\theta)$

now we have

$E = \int \frac{k(\sigma 2\pi R sin\theta Rd\theta)Rcos\theta}{R^3}$

$E = \int \frac{\sigma sin\theta cos\theta d\theta}{2\epsilon_0}$

$E = \frac{\sigma}{4\epsilon_0}$

so here we have two spherical shells of opposite charge

so net electric field at the center of the shell will be given as

$E = \frac{\sigma}{2\epsilon_0}$

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Topic : Electric field due to spherical shell

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