Question

a circular conducting plate of radius a is kept in a plane of electric field e as shown in the figure.the net electric flux is
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Answer 1

Answer: it's Zero

Explanation: Because the feild is perpendicular to the normal of the plate so cos90 = 0

Answer 2

The net electric flux is BAcos x

Where A is the area of the circular plate and B is the magnetic field.

Imagine a circular plate is kept such that it makes an angle y with the magnetic field as in the figure..

Now Area vector of a surface is perpendicular to the surface.

Let A be the area vector.

• |A| = $\pi a^{2}$

Now total flux is given by B.A = BAcos x

• Therefore, Net flux  = $\pi a^{2}$B cos x

• if x = 0, then  the plate is perpendicular to the field. Then maximum number of field lines will pass through the plate. Hence its flux will be maximum. Flux  = BA
• If x= 90 ie, y = 0, the plate will be along the magnetic field. Then no field line will cut the area of the plate and hence its flux will be zero, as cos 90 = 0