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Vandaag is het 18 January 2018

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Voltage voodoo - science puzzle

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In the figure, an electrical circuit is drawn. In the middle of the circuit a infinitely long metal bar is placed indicated with the grey circle. In this bar, an oscillating magnetic field is induced by a coil which is attached somewhere to the bar. Two resistors are located in the circuit with values R1 and R2. The alternating voltages V1 and V2 are being measured with two perfect alternating voltages meters.

What is the relation between the two voltages V1 and V2?
a) V1 : V2 = R2 : R1
b) V1 : V2 = 1 : 1
c) V1 : V2 = R1 : R2
d) V1 = V2 = 0
e) something different.
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Explanation

Answer c) is the right one, the relation is V1 : V2 = R1 : R2. This answer may sound strange because this implies that in this example it makes difference where you place your voltage meter! The strange effect is caused by the alternating magnetic field inside the electrically circuit. An alternating magnetic field causes a current inside the inner loop and hence a voltage over the resistors R1 and R2. In this case it no longer holds (as does it usually) that the voltage in a closed loop adds up to zero. Using Faraday's law you can show that V1 + V2 = - the change of the magnetic flux per time unit inside the closed loop.
To calculate the voltage over the resistors R1 and R2, you just can use the law of Ohm. The current I in the inner loop is everywhere equal. So V1 = R1 * I and V2 = R2 * I. From this it follows that V1 : V2 = R1 : R2, so answer c is right.