Electric field, direction and magnitude

[minifhncc]

Homework Statement

A rod 14.0 cm long is uniformly charged and has a total charge of -22.0μC. Determine
(a) the magnitude and
(b) direction of the electric field along the axis of the rod at a point 36.0 cm from its centre.

[I can do (b)]

Homework Equations

Electric field at the point due to a small element, ΔE=(k Δq)/(x^2)

The Attempt at a Solution

I got down to the total field at P being,
(kQ/l) * integral of 1/x^2 from x=0.29 and x=0.43

and I get 6.17 * 10^5 NC^-1

But the answer says 1.59 * 10^6 NC^-1

Are the answers wrong?

 

[ehild]

The given answer is right, how did you get that wrong value?

ehild

 

[minifhncc]

how did you get that wrong value?

(kQ/l) * integral of 1/x^2 from x=0.29 and x=0.43

= 8.9876* 10^9 * -22 * 10^-6 / 0.14 ... etc

 

[ehild]

(kQ/l) * integral of 1/x^2 from x=0.29 and x=0.43

= 8.9876* 10^9 * -22 * 10^-6 / 0.14 ... etc

And what is in place of etc?

ehild

 

[graphene]

I don't think you have considered the direction of E.
E is a vector, and you need to treat the two components separately.
Check any book for the field due to a wire, and you'll understand what you've missed.

 

[ehild]

It depends what is meant on "axis of the rod". It should be the straight line along the rod.

ehild