I would really appreciate if you could explain each step. Thank you in advance!

Question

I would really appreciate if you could explain each step. Thank you in advance!

PROBLEM 2: A long, thin rod of uniform density has a length L and a mass density The rod lies in the plane of this piece of paper, and is attached to the floor by a hinge at point P. A uniform magnetic field, of magnitude B, is directed perpendicular to the plane of this piece of paper. The rod itself is carrying a current of value i and is motionless. (a) What is the angle between the rod and the ground? Express your answer in terms of the following variables: L, , B, and/or i

Explanation / Answer

Here,

as the magnetic force acting on the rod is

FB = B *i*L

part A)

balancing the torque on the rod about the point P

B*i*L * L/2 - * L * g * L/2 * cos() = 0

B*i - * g* cos() = 0

cos() = B*i/( * g)

= arccos(B*i/( * g))

the angle is arccos(B*i/( * g))

b)

= arcos(0.031 * 3.8/(12 *10^-3 *10^2* 9.8))

= arcos(0.01008)

= 89.4 degree

the angle will be 89.4 degree

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