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A magnet in the form of a cylindrical rod has a length of 5.00cmand a diameter of1.00cm. It has a uniform magnetization of5.30×103A/m. What is its magnetic dipole moment?

Short Answer

Expert verified

The magnetic dipole moment is 2.08×10-2J/T.

Step by step solution

01

Listing the given quantities 

Length of cylinder,l=5.0×10-2m

Diameter of cylinder,2r=1.0×10-2m

Magnetization,M=5.3×103A/m

02

Understanding the concepts of magnetization

We know that magnetic moment per unit volume is magnetization. We can find the magnetic dipole moment by substituting the given values in the formula for magnetization.

Formula:

μ=Mâ‹…Ï€°ù2l

03

 Step 3: Calculations of the magnetic dipole moment

Magnetization is given by

M=μV

Where,Vis the volume and μis the magnetic dipole moment

The volume of the cylinder is given byV=Ï€°ù2l

Therefore,

M=μV=μπ°ù2l

Rearranging the above equation, we get,

μ=Mâ‹…Ï€°ù2l=(5.3×103)×π×(0.5)2×10−4×5.0×10−2=2.08×10-2J/T

The magnetic dipole moment is 2.08×10-2J/T.

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Most popular questions from this chapter

Earth has a magnetic dipole moment of μ=8×1022J/T. (a) What current would have to be produced in a single turn of wire extending around Earth at its geomagnetic equator if we wished to set up such a dipole? Could such an arrangement be used to cancel out Earth’s magnetism (b) at points in space well above Earth’s surface or (c) on Earth’s surface?

: Assume the average value of the vertical component of Earth’s magnetic field is43μT (downward) for all of Arizona, which has an area of 2.95×105km2. (a)What is the magnitude and (b) What is the direction (inward or outward) of the net magnetic flux through the rest of Earth’s surface (the entire surface excluding Arizona)?

What is the measured component of the orbital magnetic dipole moment of an electron with the values (a) ml=3 and (b)ml=−4?

Two wires, parallel to a z-axis and a distance 4rapart, carry equal currents i in opposite directions, as shown in Figure. A circular cylinder of radius r and length L has its axis on the z-axis, midway between the wires. Use Gauss’ law for magnetism to derive an expression for the net outward magnetic flux through the half of the cylindrical surface above the xaxis. (Hint: Find the flux through the portion of the xzplane that lies within the cylinder.)

(a) What is the measured component of the orbital magnetic dipole moment of an electron withml=1?(b) What is the measured component of the orbital magnetic dipole moment of an electron withml=-2?

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