Question

Problem 83

Answer 1

Given information

Given, a uniform conducting rod of length  and mass m sits atop a fulcrum, which is placed a distance  from the rod.

Uniform magnetic field of magnitude B directed into the page. An object whose mass M is 6.0 times greater than the rod’s mass is hung from the rod.

We are asked to find the current through the rod in order for it to be balanced on the fulcrum.

Step-by-step explanation

Step 1.

The magnetic and gravitational force along the rod is uniform, so we consider the two forces are acting at the center of mass of the rod.

For the balancing condition, the net torque about the fulcrum must be zero.

  

We have  

 

So here, applying the condition

 

We get,

 

 

Where is the force exerted by the magnetic field

 

So,