Question

an infinite line charge produces a field of 9 into 10 to the power 4 Newton per column at distance of 2 cm calculate the linear charge density

Answer 1

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Answer 2

Answer:

The linear charge density is $\bold{\lambda=10 \mu c m^{-1}}$

Explanation:

Given:

$\epsilon=9 \times 10^{4} N C^{-1}$

Distance of the charge =2m=d

Now consider the linear charge density $\bold{\frac{\lambda}{m}}$

We know that the linear charge density at a distance d is given by,

$t=\frac{\lambda}{2 \pi \epsilon_{o} d}$ …………eqn1

Here λ is the linear charge density,  

$\epsilon_{o}$ is the permittivity in the free space= $8.85 \times 10^{-12} n^{-1} m^{-2} c^{2}$

d is the distance

So from the (1) we have

$\lambda=t \times 2 \times \pi \in_{o} d$

Substitute the known values we get,

$\lambda=9 \times 10^{4} \times 2 \times 3.14 \times 8.85 \times 10^{-12}$

By simplifying

$\bold{\lambda=10 \mu c m^{-1}}$