Question

An infinite line of charge produces a field of magnitude 1.7×104 N/C at distance 9 m. Find the field magnitude at distance 2 m.​

Answer 1

The field magnitude at distance 2 m is $7.6\times 10^4\ N/C$.

Given :

Magnetic field at a distance 9 m from infinite line of charge is $1.7\times 10^4 \ N/C$.

We need to find the magnitude at distance 2 m.​

We know ,

Electric field due to infinite line charge is :

$E=\dfrac{\lambda}{2\pi \epsilon_o d }$      ......( 1 )

Here , $\lambda$ is linear charge density and $\epsilon_o$ is permittivity of free space and equal to $8.85\times 10^{-12} \ C^2\ m^{-2}\ N^{-1}\ .$

So ,

$\lambda=E(2\pi \epsilon_o)d$

Putting all these in above equation :

We get ,

$\lambda=1.7\times10^4\times2\times3.14 \times 8.85\times 10^{-12} \times 9$

$\lambda=8.5\times 10^{-6}\ C/m\ .$

Now , to find the field at 2 m .

Putting d = 2 m and $\lambda=8.5\times 10^{-6}\ C/m$ in equation 1 .

We get ,

$E=\dfrac{8.5\times 10^{-6}}{2\times 3.14 \times 8.85\times 10^{-12} \times 2 }$

$E=7.6\times 10^4\ N/C$

Hence , this is  the required solution .

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Electrostatics

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