Induced Emf and Magnetic Flux
Learning Objectives
By the end of this section, you will be able to:- Calculate the flux of a uniform magnetic field through a loop of arbitrary orientation.
- Describe methods to produce an electromotive force (emf) with a magnetic field or magnet and a loop of wire.
The apparatus used by Faraday to demonstrate that magnetic fields can create currents is illustrated in Figure 1. When the switch is closed, a magnetic field is produced in the coil on the top part of the iron ring and transmitted to the coil on the bottom part of the ring. The galvanometer is used to detect any current induced in the coil on the bottom. It was found that each time the switch is closed, the galvanometer detects a current in one direction in the coil on the bottom. (You can also observe this in a physics lab.) Each time the switch is opened, the galvanometer detects a current in the opposite direction. Interestingly, if the switch remains closed or open for any length of time, there is no current through the galvanometer. Closing and opening the switch induces the current. It is the change in magnetic field that creates the current. More basic than the current that flows is the emfthat causes it. The current is a result of an emf induced by a changing magnetic field, whether or not there is a path for current to flow.



Φ = BA cos θ,
where B is the magnetic field strength over an area A, at an angle θ with the perpendicular to the area as shown in Figure 5. Any change in magnetic flux Φ induces an emf. This process is defined to be electromagnetic induction. Units of magnetic flux Φ are T ⋅ m2. As seen in Figure 4, B cos θ = B⊥, which is the component of B perpendicular to the area A. Thus magnetic flux is Φ = B⊥A, the product of the area and the component of the magnetic field perpendicular to it.
Section Summary
- The crucial quantity in induction is magnetic flux Φ, defined to be Φ = BA cos θ, where B is the magnetic field strength over an area A at an angle θ with the perpendicular to the area.
- Units of magnetic flux Φ are T ⋅ m2.
- Any change in magnetic flux Φ induces an emf—the process is defined to be electromagnetic induction.
Conceptual Questions
1. How do the multiple-loop coils and iron ring in the version of Faraday’s apparatus shown in Figure 1 enhance the observation of induced emf?
2. When a magnet is thrust into a coil as in Figure 2(a), what is the direction of the force exerted by the coil on the magnet? Draw a diagram showing the direction of the current induced in the coil and the magnetic field it produces, to justify your response. How does the magnitude of the force depend on the resistance of the galvanometer?
3. Explain how magnetic flux can be zero when the magnetic field is not zero.
4. Is an emf induced in the coil in Figure 5 when it is stretched? If so, state why and give the direction of the induced current.
Figure 5. A circular coil of wire is stretched in a magnetic field.

Problems & Exercises
1. What is the value of the magnetic flux at coil 2 in Figure 6 due to coil 1?
Figure 6. (a) The planes of the two coils are perpendicular. (b) The wire is perpendicular to the plane of the coil.

2. What is the value of the magnetic flux through the coil in Figure 6(b) due to the wire?
Glossary
- magnetic flux:
- the amount of magnetic field going through a particular area, calculated with Φ = BA cos θ where B is the magnetic field strength over an area A at an angle θ with the perpendicular to the area
- electromagnetic induction:
- the process of inducing an emf (voltage) with a change in magnetic flux
Exercises
1. ZeroLicenses and Attributions
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