Video: Calculating the Magnetic Dipole Moment of a Rectangular Current Loop

A 4.0-cm by 6.0-cm rectangular current loop carries a current of 10 A. What is the magnetic dipole moment of the loop?

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Video Transcript

A 4.0-centimeter by 6.0-centimeter rectangular current loop carries a current of 10 amps. What is the magnetic dipole moment of the loop?

We’ll call the current of 10 amps 𝐼. We want to solve for the magnetic dipole moment of the loop. We’ll call this magnetic dipole moment 𝜇. And let’s start by drawing a diagram of this rectangular loop.

Here is our loop and with an area we’ll call 𝐴 carrying a current 𝐼. To solve for the magnetic dipole 𝜇, we can recall a mathematical relationship connecting these three properties. The magnetic dipole moment of a current-carrying loop 𝜇 is equal to the current in the loop multiplied by the area that it covers. We’re told that the loop is 6.0 centimeters by 4.0 centimeters, from which we can get the area 𝐴. And that the current in the loop 𝐼 is 10 amps.

When we plug these values into our equation, being careful to use units of meters for both our dimensions, and multiply the values together, we find that 𝜇, to two significant figures, is 0.024 amps meter squared. That’s the magnetic dipole moment of this current-carrying loop.

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