The plane of a square loop of wire with edge length a=0.200...

The plane of a square loop of wire with edge length $a=0.200 \mathrm{~m}$ is perpendicular to the Earth's magnetic field at a point where $B=15.0 \mu \mathrm{T}$, as shown in Figure P31.57. The total resistance of the loop and the wires connecting it to the galvanometer is $0.500 \Omega$. If the loop is suddenly collapsed by horizontal forces as shown, what total charge passes through the galvanometer?

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Key Concepts

Magnetic Flux

Magnetic flux is a measure of the quantity of magnetism, taking account of the strength and the extent of a magnetic field. It is defined as the product of the magnetic field component perpendicular to a given surface and the area of that surface, providing an indication of how many magnetic field lines pass through the area.

Faraday's Law of Induction

Faraday's law states that any change in the magnetic flux through a circuit induces an electromotive force (emf) in that circuit. This induced emf is proportional to the rate of change of the flux, and when integrated over time, it relates to the total charge that moves through the circuit.

Ohm's Law

Ohm's law connects the voltage (or emf), current, and resistance in a circuit, establishing that the current is equal to the voltage divided by the resistance. In transient situations where an emf is induced by changing flux, integrating the current over time yields the total charge, which can be calculated by dividing the net change in flux by the circuit resistance.

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