To determine The total charge on the annulus . Explanation Write the expression for the electric field, E → = − ∇ V → (I) Here, E is the electric field, and V is potential. Write the expression for the electric potential at point x due to the annulus. V ( x ) = − 2 k π σ ( b 2 + x 2 − a 2 + x 2 ) = 2 k π σ ( a 2 + x 2 − b 2 + x 2 ) (II) Here, σ is the charge density, a , b is the distance of the inner and outer annulus circle from the centre, and x is the point where the potential is calculated. Write the expression for charge on a conducting spheres surface, Q = π ( r b 2 − r a 2 ) σ (III) Conclusion Substitute expression (II) in expression (I), and differentiate the expression, E → = 2 k π σ d d x ( a 2 + x 2 − b 2 + x 2 ) = 2 k π σ ( 1 2 x 2 + a 2 2 x − 1 2 x 2 + b 2 2 x ) = 2 k π σ ( x a 2 + x 2 − x b 2 + x 2 ) Substituting 0

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ISBN: 9780134988566

Author: Wolfson, Richard

Publisher: Pearson Education,

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One of the fundamental properties is the electromagnetic property. Charge cannot be destroyed by any process and this contributes formally to the law of charge conservation.

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Chapter 22, Problem 38E

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The total charge on the annulus .

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Chapter 22, Problem 37E

Chapter 22, Problem 39P

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