A simple pendulum with bob of mass m and conducting wire of length L swings(is hanging ) under gravity thro' an angle 2theetha.

The earth's magnetic feild component in the direction perpendicular to swing is B.

the max potential diff induced across pendulum is?

To calculate the maximum potential difference induced across the pendulum, we need to consider the relationship between the magnetic field (B), mass (m), length (L), angle of swing (θ), and the gravitational field (g).

The potential difference induced across the pendulum can be determined using the equation:
V = B * L * v,

where V is the induced potential difference, B is the magnetic field component perpendicular to the swing, L is the length of the conducting wire, and v is the velocity of the pendulum bob.

To find the velocity of the pendulum bob, we can use the conservation of mechanical energy. The total energy of the pendulum is the sum of its kinetic energy and potential energy. At the maximum angle (θ), all the energy is in the form of potential energy, half of which is converted into kinetic energy at the bottommost point of the swing.

The potential energy of the pendulum at the maximum angle is given by:
PE = m * g * L * (1 - cosθ).

At the bottommost point, the potential energy is completely converted to kinetic energy:
KE = m * g * L * (1 - cosθ).

Using the principle of conservation of energy, we can equate PE and KE:
m * g * L * (1 - cosθ) = 0.5 * m * v^2.

Simplifying this equation, we have:
v = √(2 * g * L * (1 - cosθ)).

Now that we have the value of v, we can substitute it into the initial equation to find the induced potential difference:
V = B * L * v.

Please provide numerical values for the mass (m), length (L), angle of swing (θ), and the magnetic field component (B) for a specific calculation.