A student makes a short electromagnet by winding 300 turns...

A student makes a short electromagnet by winding 300 turns of wire around a wooden cylinder of diameter $d=5.0 \mathrm{~cm} .$ The coil is connected to a battery producing a current of $4.0 \mathrm{~A}$ in the wire. (a) What is the magnetic moment of this device? (b) At what axial distance $z$ ? $d$ will the magnetic field of this dipole have the magnitude $5.0 \mu \mathrm{T}$ (approximately one-tenth that of the Earth's magnetic field)?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Magnetic Moment

The magnetic moment is a measure of the strength and orientation of a magnetic source. For a coil, it is calculated as the product of the number of turns, the current flowing through the coil, and the area of one loop. This parameter is crucial because it determines the torque experienced by the coil in an external magnetic field as well as the strength of the field it produces.

Magnetic Field of a Dipole

The magnetic field of a dipole, especially along its axial line, decreases with the cube of the distance from the dipole. This relationship is typically expressed by a formula that includes the permeability of free space and the dipole’s magnetic moment. Understanding this concept is essential for determining how the magnetic field strength diminishes with distance, which is important in applications ranging from electromagnets to planetary magnetic fields.

Area of a Coil

The area of a coil, particularly when dealing with circular loops, plays a key role in calculating the magnetic moment. It is determined by using the formula for the area of a circle, which involves the square of the radius. This concept is fundamental because the coil’s geometric dimensions directly affect its electromagnetic properties and the strength of the magnetic field it can generate.

Transcript

Please give Ace some feedback