Question

The electric field 'E' is uniform in the shaded area and makes an angle θ with the normal. The conductivity of the material in which the area 'S' lies is σ. The electric current flowing out of the shaded area is

Answer 1

Answer ⇒ i = σESCosθ

Explanation ⇒ Area vector is always normal to the surface of the object.

By giving an angle, they actually means that angle between area vector and the Electric field is given.

Now, By Ohm's law,

  j = σE

Now, We know that Current is the dot product of Current density and Area vector.

∴ i = jSCosθ

Thus, j = i/SCosθ

∴ i/SCosθ = σE

∴ i = σESCosθ

''Thus, Electric current flowing in the Shaded area is σESCosθ.''

Hope it helps.