Lenz Law

We need to determine the current required to keep a metallic rod stationary on a smooth inclined plane at an angle of in a vertical magnetic field.

Step 1: Forces Acting on the Rod

• Gravitational force acting downward.
• Magnetic force due to current in the rod.

Step 2: Component of Gravitational Force

The component of weight along the plane is:

Given mass per unit length , for unit length:

Step 3: Magnetic Force

For unit length :

Step 4: Equilibrium Condition

Conclusion: The required current is .