A magnetic field force question?

To get the magnitude of the force, you can use sin(70°).

Note, in any case, sin(70°) = sin(110°).

Your calculation is correct. the formula is simply

||F|| =B.I.L.sin(θ)

E.g see link.

So it looks like the book is wrong - it happens.

A cable 100 m long

carries current of 50 A

and is pointing due magnetic north

and the magnetic field is 70 degs to the horizontal at this point.

The cable is horizontal to the ground ..

what is the force exerted by the magnetic field on the cable..

my problem is the answer given in the book seems incorrect..

dF = Idl x B

I get this as the magnetic field of the earth will be constant over the length of the wire please tell me if this assumption is incorrect.

0.5*10^-4 T

since current is constant.. and angle is constant.. the formula should simplify to

F = I * L * B * sin theta..

since the cross product is the first turned into the second so that the angle is not 70 degs but 110 degs rotation between the current and the B field.

F = 50*100*0.5*10^(-4) * sin(110)

F = 0.235 N

can you verify this answer the books answer is

F = 7.15*10^-1 N which I think is incorrect..