3. A square loop of wire with an area of 2.5x10-3 m2 is perpendicular to a uniform magnetic field (B= 2.2x10-2 T). If the square collapses (collapsed area=0) in a time of 0.100 s as shown in the diagram what is the average induced emf as it is collapsed and what is the direction of the induced current? (Remember to use conventional current)
\(\epsilon =\frac{\Delta \phi }{\Delta t}=\frac{\left[\left(2.5\times 10^{-3}\right)\left(2.2\times 10^{-2}\right)\right]}{0.100}=5.5\times 10^{-4}\) V [clockwise]
5. A magnet is quickly removed from a circular coil (25 turns, area = 5.0 x 10-3 m2) changing the magnetic field within the coil at a rate of 0.40 T/s. What is the average emf induced in the coil?
\(emf=-N\frac{\Delta \phi }{\Delta t}\)
\(N = 25\)
\(emf=\epsilon =25\frac{\left(5.0\times 10^{-3}\right)\cdot \left(0.40\right)}{1}=0.05=5.0\times 10^{-2}\) V
5. A conducting rod in the diagram below is 30.0 cm long and is moved perpendicular to 0.950 T magnetic f . If the resistance in the circuit is 3.25 ohms what force is required to move the rod at a constant 1.5 m/s?
B = 0.950 T
R = 3.25 ohms
V = 1.5 m/s
L = 30.0 cm to 0.300 m
ε = vBL
ε = (1.5)(0.950)(0.300)
ε = 0.4275
I = current = ε/R = 0.4275/3.25 = 0.13153 A As the rod is moving to the right, the flux in the region
defined by the rod, the rails and the load is increasing. By Lenz’s law, the current must be counter-clockwise if its magnetic field is to counter this increase in flux.
The net force on the rod ∑F = Fapp − Fm = 0, where Fapp is the applied force and Fm is the magnetic force.
∴ The force on a section of wire of length L carrying a current I through a magnetic field B is
Fapp = Fm = I (L*B) (from earlier).
F = 0.13153 A * 0.300 m * 0.950 T =
0.0375 N
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