Define magnetic flux - Leaving Cert Physics - Question 12(b) - 2005

Faraday's law states that the magnitude of the electromotive force (e.m.f.) induced in a conductor is proportional to the rate of change of magnetic flux through the conductor. Mathematically, this can be represented as:

$$\text{e.m.f.} = -\frac{d\Phi}{dt}$$

This indicates that a change in magnetic field within a closed loop induces an e.m.f. in that loop.

To calculate the magnetic flux ( (\Phi)) cutting the coil, we need to first determine the area (A) of the square coil:

• Side length: 5 cm = 0.05 m
• Area:

$$A = (0.05 \, ext{m})^2 = 0.0025 \, ext{m}^2$$

Using the magnetic flux formula:

$$\Phi = B \cdot A = (4.0 \, ext{T}) \cdot (0.0025 \, ext{m}^2) = 0.01 \, ext{Wb}$$

To find the average e.m.f. ( (E)) induced in the coil, we use the formula:

$$E = -N \frac{\Delta \Phi}{\Delta t}$$

where:

• (N = 200) turns,
• (\Delta \Phi = \Phi_{final} - \Phi_{initial} = 0 - 0.01 , ext{Wb} = -0.01 , ext{Wb})
• Time (\Delta t = 0.2 , ext{s})

Calculating:

$$E = 200 \cdot \frac{|\Delta \Phi|}{0.2} = 200 \cdot \frac{0.01}{0.2} = 10 \, ext{V}$$

Thus, the magnitude of the average e.m.f. induced in the coil is 10 V.