Question

An infinite line of charge with linear density of charge, X = 2.0 x 10-6 C/m exists. The electrostatic force on a point charge of 5.0 mC at a distance of 50 cm from the line of charge will be​

Answer 1

let us consider the Gaussian surface around the charge is cylindrical.

Now clearly from the figure flux is acting on the curved surface area only.

Applying Gauss Theorem,

Answer 2

Given:

An infinite line of charge with linear density of charge, X = 2.0 x 10-6 C/m exists.

To find:

The electrostatic force on a point charge of 5.0 mC at a distance of 50 cm from the line ?

Calculation:

Force can be calculated as the product of electrostatic field intensity and the charge present at that point.

$\rm\therefore \: F = q \times E$

$\rm \implies \: F =( 5 \times {10}^{ - 3}) \times \dfrac{2k \lambda}{d}$

$\rm \implies \: F =( 5 \times {10}^{ - 3}) \times \dfrac{2 \times (9 \times {10}^{9}) \times (2 \times {10}^{ - 6}) }{ \frac{50}{100} }$

$\rm \implies \: F =( 5 \times {10}^{ - 3}) \times 4 \times (9 \times {10}^{9}) \times (2 \times {10}^{ - 6})$

$\rm \implies \: F = 360 \: N$

So, net force experienced by charge is 360 N.

_______________________

• The field intensity formula can be calculated by Gauss's Law using a cylindrical Gaussian Surface.

• E = $\dfrac{2k\lambda}{d}$, lambda is the linear charge density, k is $\dfrac{1}{4\pi\epsilon_{0}}$ and 'd' is distance from infinite wire.