# PHYS 2212 Module 9.1

### Learning Objectives

By the end of this section, you will be able to:

• Determine the magnetic flux through a surface, knowing the strength of the magnetic field, the surface area, and the angle between the normal to the surface and the magnetic field
• Use Faraday’s law to determine the magnitude of induced emf in a closed loop due to changing magnetic flux through the loop

The emf 𝜀 induced is the negative change in the magnetic flux Φm per unit time. Any change in the magnetic field or change in orientation of the area of the coil with respect to the magnetic field induces a voltage (emf).

Let’s start with defining what we mean by the word “induction.” If you look it up in the dictionary, you’d find something like “the process or action of bringing about or giving rise to something.” So when we talk specifically about Faraday’s law of induction, it describes the action of bringing about or giving rise to an emf.

Practice!

Faraday’s Law says it is only the change in flux through the loop that matters. A huge B-field (lots of flux) does NOT make the emf, it’s the change in B with time that does the trick. Since Φ = BAcosθ, you can change the flux in many ways: you could change B, or the area, or the angle between B and the loop. These changes in the flux would all result in an induced emf in the coil.

There is a minus sign in Faraday’s law, which we will discuss shortly. But I want to put aside for the moment. Suffice it to say, that minus sign tells you about the direction of the induced emf and the direction that the induced current will flow in the loop. This is called Lenz’s law, and I will discuss it in detail in the next part of the module. What we can do for now is find the magnitude of the induced emf and not worry about its direction yet.

Practice!

Two circular loops of wire with small bulbs in them are sitting beside two long straight current-carrying wires. The loops with the bulbs have no battery or power supply, they are simply wires with bulbs. The long straight wires are connected to batteries not shown, but that is where the currents I1 and I2 come from. Recall from the last module that currents in a long straight wire produce magnetic fields that circulate around them with a magnitude of . The wire loops, bulbs, and long straight wires are identical for the two cases. The loops are the same distance from the straight wires. But situation A is isolated from situation B, they have no effect on each other. We are going to look at different scenarios and predict what will happen to the bulb.

In each of the following questions, determine if the bulbs will light up.

Practice!