EK 1001 Physics problem #880

[wahcha]

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Hey guys I don't understand ANYTHING about this question:

A conducting bar is slid at a constant velocity v along two parallel conducting rods. The rods are separated by a distance L and connected across a resistor R. The entire apparatus is placed in an external magnetic field B directed into the page.

-------
R C
-------
R = resistor, C = conducting bar. --- = conducting rod

Which of the following represents the current generated by the apparatus?

Answer: current remains constant


The solution manual states: "Faraday's law is the easiest way to visualize the current. Since the bar is moving at constant velocity, the area of the loop is increasing at a constant rate, and the flux also increases at a constant rate. From Faraday's law, the current is constant."


I have no idea what they're talking about. As you slide the conducting bar...more magnetic flux is felt by the circuit, no? (more area on the circuit to be affected by the flux) I reasoned this would increase the the EMF... which increases I in V=IR (not sure if v=ir applies to EMF, my magnetism is horrible) This question wrecked my concept of Faraday's law as well. Someone save me?

 

[wolverinepwns]

Hey guys I don't understand ANYTHING about this question:

A conducting bar is slid at a constant velocity v along two parallel conducting rods. The rods are separated by a distance L and connected across a resistor R. The entire apparatus is placed in an external magnetic field B directed into the page.

-------
R C
-------
R = resistor, C = conducting bar. --- = conducting rod

Which of the following represents the current generated by the apparatus?

Answer: current remains constant


The solution manual states: "Faraday's law is the easiest way to visualize the current. Since the bar is moving at constant velocity, the area of the loop is increasing at a constant rate, and the flux also increases at a constant rate. From Faraday's law, the current is constant."


I have no idea what they're talking about. As you slide the conducting bar...more magnetic flux is felt by the circuit, no? (more area on the circuit to be affected by the flux) I reasoned this would increase the the EMF... which increases I in V=IR (not sure if v=ir applies to EMF, my magnetism is horrible) This question wrecked my concept of Faraday's law as well. Someone save me?

the KEY to the answer is the CONSTANT velocity, so when the velocity is constant, thus the area increase rate is constant too, the current will be constant. think of it in case of F=ma, constant velocity leads to zero accelration and thus zero Force, so there is no increase in the Force to push for a change in the current! if the area of the rod was increasing faster or slower than the flux then current would change but due to the constant velocity this isn't the case so the current stay constant.

 

[Rabolisk]

Faraday's law of induction basically says that emf on a closed circuit is equal to the rate of change of magnetic flux through the circuit, or the derivative of magnetic flux. Magnetic flux is the integral, or sum of the magnetic field through the surface (area enclosed by the circuit). That means you can change flux by either changing magnetic field or changing the area (this problem). However, if you increase or decrease the length of a rectangle at a constant rate, then the area also increases at a constant rate. That means that the magnetic flux changes at a constant rate, resulting in constant emf. Constant emf must mean constant current, since the resistance does not change.

 

[wahcha]

So EMF = rate of change in magnetic flux (Faraday's Law)

Since the rate of change remains constant, EMF remains constant and as does current. Got it, thanks for the help!