50 cm long wire is carrying a current of 1.5A at 30° North of West in a magnetic field of 2 T oriented South. Determine the magnitude and direction of the force acting on the wire.  This is a question I've been stuck on, I'm not sure If I'm right.  So I did:   0.5 x 1.5 x 2 x sin 30  = 0.75 N, up (according to right hand rule).  Am I right? 

Expert Answers

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It has used the right formula, but it has not replaced the correct angle. Note that the magnetic field is directed to the South and the electric current to 30 degrees over the West direction. In these conditions the angle between the current and the field is:

Ɵ = 90° + 30° = 120°

According to Ampere equation for the magnetic force, in this case we have:

Fm = I (l x B)

When the vector product is decompose, we have:

Fm = I*l*B*sin 120°

Substituting the values:

Fm = (1.5)(0.5)(2)(0.86)

Fm = 1.3 N

According to the right hand rule, this force is directed upwards and perpendicular to the surface of the Earth.

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