We have to calculate expressions for the following four quantities, considering both and :

(a) for a current in a long wire of radius ;

(b) for a long uniform cylinder of charge of radius ;

(c) for a parallel-plate capacitor, with circular plates of radius , in which is changing at a constant rate; and

(d) for a cylindrical region of radius in which a uniform magnetic field is changing at constant rate.

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(a)

For finding for a current in a long wire of radius we will use Ampere’s law

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(b)

We will use Gauss’ law for finding for a long uniform cylinder of charge of radius .

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Let the charge per unit length on the cylindrical wire of radius be . We consider a cylindrical Gaussian surface of length l and radius r. We have

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(c)

We will use Ampere’s law (version extended by Maxwell) for finding for a parallel-plate capacitor, with circular plates of radius , in which is changing at a constant rate.

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(d) We will find for a cylindrical region of radius in which a uniform magnetic field is changing at constant rate using Faraday’s law

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Case :