Question

in a long wire of round cross section of radius r varies with radial distance from axis of wire x as J =cx2 a/m2 find total current flowing throgh wire​

Answer 1

Answer:

As we learnt

If current density is not uniform -

I=\int \vec{J}\cdot d\vec{A}

- wherein

The direction for J is usually in the direction of E-field.

I = ∫ j.dA = ∫kr.2∏r dr = 2∏k∫r2 dr = 2∏R3k/3

Option 1)

∏R2k

Option 2)

∏R3k

Option 3)

2∏R3k/3

Option 4)

∏R2k/3