Question

Q.16 a point charge +2q is placed at a distance of 8 cm from centre of a disc (on the axis of disc) having radius r = 6 cm. Total electric flux passing through this disc is

Answer 1

Given:

A point charge +2q is placed at a distance of 8 cm from centre of a disc (on the axis of disc) having radius r = 6 cm.

To find:

Total electric flux passing through this disc is?

Solution:

Let us consider,

A point charge "q" is placed at a distance d from the center of circular disc of radius R.

Flux through the circular disc by Gauss law

Ф = ain/∈₀

⇒ Ф = q/∈₀

Solid angle about a point in circular disc = 4π

Solid angle at the tip of the cone Ω = 2π (1 - cosθ)

Flux through 4π solid angle Ф = q/∈₀

Flux through Ω  = 2π (1 - cosθ)

Solid angle Ф = q/4π∈₀  [2π (1 - cosθ)]

⇒ Ф = q/2∈₀  (1 - cosθ)

∴ Flux through the disc Ф = q/2∈₀  {1 - d/√[d² + R²]}

Now consider,

From given, we have,

q = +2q

d = 8  cm

R = r = 6 cm

∴ Flux through the disc Ф = q/2∈₀  {1 - d/√[d² + R²]}

Ф = 2q/2∈₀  {1 - 8/√[8² + 6²]}

Ф = q/∈₀  {1 - 8/√[100]}

Ф = q/∈₀  {1 - 8/10}

Ф = q/∈₀  {2/10}

Ф = q/∈₀  {1/5}

∴ Ф = q/5∈₀        (where, ∈₀ = 8.854 × 10^{-12} F.m-1)

substituting the value of ∈₀, we get,

Ф = q × 2.258 × 10^{10}

Total electric flux passing through this disc is q(2.258 × 10^{10})