A 10.0-cm diameter hemisphere lies within a uniform electric field of magnitude 1000NC and direction perpendicular to the flat side of the hemisphere. The hemisphere contains no charge, and the flux through the base is in the outward direction. The flux through the rounded portion of the surface is

Φcurved= 7.86 Nm²/C

Φbase= -7.86 Nm²/C

Explanation:

Given that

diameter of the hemisphere is 10cm

Radius =diamter/2

Radius = 10/2 =5cm =0.05m

Electric field =1000N/C.

1. Flux=? At the base

Let choose a coordinate system where the origin is at the center of the base, such that the base is in the xy plane

Flux is given as

Φ=E×A

The area of the base hemisphere is a circle and it is given as πr²

Then,

Φ=- πr²E k

Φ=- 3.142×0.05²×1000 k

Φ=-7.86 k Nm²/C

It is in the negative direction of the z half space plane

2. Flux=? At the curved surface

The flux the base is equal to negative of the flux at the curved since the entire flux in the enclosed system is zero

Therefore

Φbase + Φcurved= 0

Φcurved=-Φbase

Then,

Φcurved= -(-7.86 k Nm²/C)

Φcurved= 7.86 k Nm²/C

measure their densities same density, same sub