Magnetic Potential Energy and Dipole Dynamics in Uniform Magnetic Fields

Professor Rahe introduces magnetic potential energy, explaining how a dipole in a uniform magnetic field experiences torque due to equal and opposite forces. The work done by this torque is stored as potential energy. The video covers the calculation of work done using integration, deriving expressions for magnetic potential energy, and discussing equilibrium positions of a dipole in a magnetic field.

What is the effect of placing a dipole in a uniform magnetic field?

• It loses its magnetic properties.

• It aligns itself parallel to the magnetic field.

• It remains unaffected by the magnetic field.

• It experiences a torque due to equal and opposite forces.

How is work done related to torque in rotational motion?

• Work done is equal to torque plus angular displacement.

• Work done is equal to torque multiplied by angular displacement.

• Work done is independent of torque.

• Work done is equal to torque divided by angular displacement.

Why is it necessary to integrate torque over angular displacement?

• Because torque is a variable quantity.

• Because work done is not related to torque.

• Because torque is a constant quantity.

• Because angular displacement is always zero.

What is the expression for magnetic potential energy derived from integration?

• um = mb(cot θ₀ - cot θ)

• um = mb(cos θ₀ - cos θ)

• um = mb(sin θ₀ - sin θ)

• um = mb(tan θ₀ - tan θ)

What happens to magnetic potential energy when a dipole is placed perpendicular to the magnetic field?

• It becomes zero.

• It becomes maximum.

• It becomes negative.

• It becomes undefined.

What is the magnetic potential energy when a dipole is parallel to the magnetic field?

• It is undefined.

• It is zero.

• It is maximum and equals mb.

• It is minimum and equals -mb.

What is the most stable equilibrium position of a dipole in a magnetic field?

• When the dipole is parallel to the magnetic field.

• When the dipole is at 45 degrees to the magnetic field.

• When the dipole is perpendicular to the magnetic field.

• When the dipole is at 180 degrees to the magnetic field.

What is the magnetic potential energy when a dipole is at 90 degrees to the magnetic field?

• It is undefined.

• It is minimum.

• It is zero.

• It is maximum.

What is the magnetic potential energy when a dipole is at 180 degrees to the magnetic field?

• It is maximum and equals mb.

• It is minimum and equals -mb.

• It is zero.

• It is undefined.

What is the most unstable equilibrium position of a dipole in a magnetic field?

• When the dipole is at 45 degrees to the magnetic field.

• When the dipole is perpendicular to the magnetic field.

• When the dipole is parallel to the magnetic field.

• When the dipole is at 180 degrees to the magnetic field.