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 -0.1 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 find the answers to these questions, we need to understand the concept of induced EMF and the relationship between induced EMF and the change in magnetic flux. Here's how you can approach it:
Step 1: Understand the Concept
In this circuit, the changing magnetic field in the shaded area induces an electromotive force (EMF) in the circuit according to Faraday's law of electromagnetic induction. The induced EMF is given by the equation:
EMF = -N * dΦ/dt
where N is the number of turns in the loop and dΦ/dt represents the rate of change of magnetic flux.
Step 2: Determine the Induced EMF
Since we don't have specific values for the number of turns and the rate of change of magnetic flux, we can't compute the exact induced EMF. However, we can determine its magnitude by using the reading of Vright, which is -0.1 Volt. The magnitude of the induced EMF is equal to the magnitude of the reading on Vright.
So, the magnitude of the induced EMF is 0.1 Volt.
Step 3: Determine the Reading of Vleft
To determine the reading of Vleft, we need to consider the direction of the current flowing in the circuit caused by the induced EMF. The internal resistances of the voltmeters are negligible compared to the external resistances.
Since the induced EMF is negative (as indicated by the negative sign in Vright), the current will flow in the clockwise direction (opposite to the conventional current direction).
In this case, the induced current will flow from the negative terminal of Vright to the positive terminal of Vright (since the "+" side of both voltmeters faces up). Therefore, Vleft will measure a positive voltage.
The magnitude of the voltage reading on Vleft, at that moment, will be equal to the magnitude of the induced EMF since the internal resistance of the voltmeters is the same (106 Ω) and the circuit has negligible internal resistance.
So, the reading on Vleft will be 0.1 Volt.
In summary:
(a) The magnitude of the induced EMF at that moment is 0.1 Volt.
(b) The reading on Vleft at that moment is 0.1 Volt.