# Induced current in a wire multiple choice question

1. Aug 7, 2006

### jubba

question In a particular experiment a long length of copper wire of very low resistance is rotated by two students. The ends of the wire are connected to a galvanometer, G, and a current is detected.

Which of the following is LEAST likely to affect the amount of current produced?
(A) The length of the rotating wire
(B) The thickness of the rotating wire
(C) The speed with which the wire is rotated
(D) Whether the wire is oriented north-south or east-west

I thought it was (A) but the answers say it is (B). Could anyone explain this.
Thanks

2. Aug 7, 2006

### Staff: Mentor

I think the question is referring to a large loop of wire. What is the equation for the induced voltage around a wire loop as the amount of magnetic flux through the loop is changing? What affects the amount of flux that is going through the loop in its various positions?

3. Aug 7, 2006

### Andrew Mason

If a current is detected, there must be a magnetic field. Since there is no mention of an applied magnetic field, we can assume that the magnetic field is that of the earth.

The galvanometer and the wire form a loop. The rate of change of magnetic flux through that loop will determine the amount of emf generated in the loop (Faraday's law).

The flux through the loop is $\phi = B\cdot A$ where A is the area of the loop including the leads and galvanometer. The area that changes, however, is the area swept out by the rotating wire.

If the vector for the area swept out by the rotating wire is parallel (remember the area vector is perpendicular to the area surface) to the magnetic field, there will be maximum flux so there will be a greater value of $d\phi/dt$ and greater current. So orientation in the earth's magnetic field will affect the emf and current produced. (D)

If the wire rotates faster, there will be more change in flux per unit time, so more emf and current. (C)

If the wire is longer, there will be more area swept per unit time (you can think of it as more flux lines 'cut' per unit time) so there will be a higher induced emf and more current. (A)

The current produced will be limited by the resistance of the galvanometer coil, which has a much higher resistance than the wire. So while the thickness of the wire will affect the resistance of the wire, it will not significantly affect the resistance of the whole circuit (B)

AM

4. Aug 8, 2006

### jubba

thanks i understand now