Question

In a region of space having a uniform electric field E, a
hemispherical bowl of radius r is placed. The electric flux ∅
through the bowl is
(a) 2πRE (b) 4πR²E
(c) 2πR²E (d) πR²E

Answer 1

Given:

In a region of space having a uniform electric field E, a hemispherical bowl of radius r is placed.  

To find:

The electric flux ∅ through the bowl is

Solution:

From given, we have,

In a region of space having a uniform electric field E, a hemispherical bowl of radius r is placed.  

Area of a hemispherical bowl = 2πr²

The electric flux is given by,  

⇒ Ф = E (ds) cos θ

Ф = E (2πr²) cos 0°

∴ Ф = 2πr²E

Option (c) 2πR²E is correct.

Answer 2

Given that,

Electric field = E

Radius = r

Electric flux = Φ

Area of the hemisphere bowl = 2πr²

We need to calculate the electric flux through the bowl

Using formula of flux

$\phi=E(ds)\cos\theta$

Where, E = electric field

Put the value into the formula

$\phi=E(2\pi r^2)\cos0^{\circ}$

$\phi=2\pi r^2E$

Hence, The electric flux through the bowl is $2\pi r^2 E$.

(c) is correct option