A uniform magnetic field of induction B is confined in a cylindrical region of the radius R . If the field is increasing at a constant rate of d B d t = α T s - 1 , then the intensity of the electric

Question

A uniform magnetic field of induction B is confined in a cylindrical region of the radius R . If the field is increasing at a constant rate of d B d t = α T s - 1 , then the intensity of the electric field induced at a point P distant r from the axis as shown in the figure is equal to

TestHub · Accepted Answer

Magnetic flux linked with circular section of radius $r$ of the cylinder , $ϕ = (π r^{2}) B .$

Due to this induced emf, an electric field E is established which is equal to potential difference per unit length.

$E = \frac{e}{2 π r} = \frac{π r^{2} α}{2 π r}$

$E = \frac{1}{2} r α$

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