Question

What will be the linear charge density of
an infinite line charge producing a
uniform field of 16 x 10' N/C at a
distance of 4 cm?​

Answer 1

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}}

4.3