Two voltmeters, Vright and Vleft, each with an internal resistance of 106 Ω are connected through wires of negligible resistance (see the circuit below). The “+" side of both voltmeters is up as shown. A changing magnetic field is present in the shaded area.
At a particular moment in time Vright reads -0.2 Volt (notice the − sign).
(a) What, at that moment, is the magnitude of the induced EMF (in Volts) in the circuit?
(b) At that moment in time, what is the reading of Vleft? (make sure you have the correct sign!)
To solve this problem, we can use Faraday's law of electromagnetic induction, which states that the induced electromotive force (EMF) in a circuit is equal to the rate of change of magnetic flux through the circuit.
(a) To find the magnitude of the induced EMF, we need to determine the rate of change of magnetic flux through the circuit. Since the magnetic field is changing in the shaded area, there will be a changing magnetic flux through the circuit.
Since there is no other information given about the circuit or the changing magnetic field, it is assumed that the circuit is a simple loop of wire. In this case, the magnetic flux through the circuit is given by the product of the magnetic field strength (B) and the area (A) of the loop.
To calculate the magnetic flux, we need to know the area of the shaded region and the magnetic field strength. Unfortunately, this information is missing in the question, so we cannot determine the magnitude of the induced EMF without further details.
(b) At that moment in time, Vleft would read the same value as Vright. The reason for this is that both voltmeters are connected through wires of negligible resistance, meaning that the potential difference between Vleft and Vright should be zero. Since Vright reads -0.2 Volt, Vleft will also read -0.2 Volt.