Question

The intrinsic magnetic dipole moment of the electron has magnitude $9.3 \times 10^{-24} \mathrm{A} \cdot \mathrm{m}^{2} .$ In other words, the electron acts as though it were a tiny current loop with $N I A=9.3 \times 10^{-24} \mathrm{A} \cdot \mathrm{m}^{2} .$ What is the maximum torque on an electron due to its intrinsic dipole moment in a \(1.0-T\) magnetic field?

Short answer

Answer: The maximum torque on an electron due to its intrinsic dipole moment in a 1.0-T magnetic field is \(9.3 \times 10^{-24} N\cdot m\).

Step-by-step solution

Write the torque formula related to magnetic dipole moment and magnetic field

We know that the torque τ acting on a magnetic dipole of magnetic moment μ in a magnetic field B is given by τ = μ * B * sin θ, where θ is the angle between the magnetic moment and the magnetic field.

Find the maximum torque

To find the maximum torque, we need the maximum value of sin θ, which is 1 when θ = 90 degrees. Therefore, the maximum torque is given by τ_max = μ * B.

Substitute the given values and calculate the maximum torque

Given, intrinsic magnetic dipole moment of the electron (μ) = \(9.3 \times 10^{-24} A\cdot m^2\) and magnetic field (B) = 1.0 T. Substitute these values into the formula: τ_max = μ * B = \((9.3 \times 10^{-24} A\cdot m^2) * (1.0 T)\). Hence, τ_max = \(9.3 \times 10^{-24} N\cdot m\). Thus, the maximum torque on an electron due to its intrinsic dipole moment in a 1.0-T magnetic field is \(9.3 \times 10^{-24} N\cdot m\).