Verified answer

In general the electric field at a distance r from a point charge q, is E = q/(4πεₒr²)

In this case the charge is spread out along the wire, so we have to treat the charge in short elements, to get quasi point charges, enabling us to apply the above formula. We can work in the y, z plane and need to add up all of the elementary horizontal (y-directed) components of field. The z-directed components will anyway cancel out by symmetry of the charge distribution;

dE = dq/[4πεₒ(z²+36)] ͯ [36/√(z²+36)] = 9.dz.(9/35)/[πεₒ(z²+36)^(3/2)]

(note: dq = (9/35).dz).

We need to integrate this from z= -35/2 to z= 35/2 or we may integrate it from 0 to 35/2 and double the answer. The latter (with a zero limit) is usually simpler.

The integral is:

81/[35.(πεₒ)].∫[1/(z²+36)^(3/2)] = 81/[35.(πεₒ)] ͯ [z/(z²+36)]/36

So just insert the limits on z and you have the answer!