Question

A proton with a magnetic field due to its spin is similar to a circular current loop. Find the maximum torque on a proton in a 2.50-T field.

a) 1.87 × 10-23 N.m
b) 2.45 × 10-23 N.m
c) 3.02 × 10-23 N.m
d) 4.11 × 10-23 N.m

Answer 1

The maximum torque on a proton in a 2.50-T magnetic field can be found using the equation T = μBsinθ, where T is the torque, μ is the magnetic moment of the proton, B is the magnetic field strength, and θ is the angle between the magnetic moment and the magnetic field. By calculating the magnetic moment and substituting it into the torque equation, we find that the maximum torque on a proton in a 2.50-T field is approximately 1.87 × 10⁻²³ N.m.

Step-by-step explanation:

To find the maximum torque on a proton in a 2.50-T magnetic field due to its spin, we can use the equation:

T = μBsinθ

where T is the torque, μ is the magnetic moment of the proton, B is the magnetic field strength, and θ is the angle between the magnetic moment and the magnetic field.

The magnetic moment of a proton is given by:

μ = I * A

where I is the current and A is the area of the circular current loop.

Given that the radius of the loop is 0.650 × 10⁻¹⁵ m and the current is 1.05 × 10⁴ A, we can calculate the magnetic moment:

μ = (1.05 × 10⁴ A)(π * (0.650 × 10⁻¹⁵ m)²)

Next, we can calculate the torque:

T = μBsinθ = (1.05 × 10⁴ A)(π * (0.650 × 10⁻¹⁵ m)²)(2.50 T)

Using a calculator, we find that the maximum torque on a proton in a 2.50-T field is approximately 1.87 × 10⁻²³ N.m.