Auniform line charge of density λ lies on the x axis between x = 0 and x = l. its total charge is 7 nc. the electric field at x = 2 l is (500 n/c)ˆı. find the electric field at x = 3 l. the coulomb constant is 8.99 × 109 n · m2 /c 2 . answer in units of n/c.

The electric field at x = 3L is 166.67 N/C

Solution:

As per the question:

The uniform line charge density on the x-axis for x, 0< x< L is

Total charge, Q = 7 nC =

At x = 2L,

Electric field,

Coulomb constant, K =

Now, we know that:

Also the line charge density:

Thus

Q =

Now, for small element:

Integrating both the sides from x = L to x = 2L

Similarly,

For the field in between the range 2L< x < 3L:

Now,

If at x = 2L,

Then at x = 3L:

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