- #1
bw519
- 5
- 2
- Homework Statement
- A simple circuit that is 0.3m wide and 0.2m tall is driven with an alternating current (AC) power supply and has a 5 ohm resistor. The AC supply applies a 20V amplitude at 60 Hz. What emf amplitude is induced in microvolts in a small 1cm square loop of wire at the center of the circuit? (you can assume the field is constant over the surface of the square)
- Relevant Equations
- Emf = NBAw
I used the voltage of the power supply and resistance to solve for the current in the larger circuit (20V/5ohms=4 amps). I am not sure if the equation listed above is the correct one I should be using, but I tried it using the following numbers. For omega, I used 2*pi*frequency. N should equal 1. For area I tried the area of the small square (0.01mx0.01m). I had more of an issue solving for B. I found equations for the magnetic field due to a circular loop and due to a long wire, but I had more trouble finding anything for a rectangular loop. Is this even the correct way to be solving this problem? If so, is there an equation for B that I should be using.
I found one video online that was solving for the B at the center of a square loop. I believe the equation was 4*(4*pi*10^-7)*I*sin(theta)/(4*pi*a/2) where a was the length of the sides of the square. I was trying to use that with the rectangular wire by summing two versions of that equation, using 2 as the first coefficient for two sides at a time that were the same length (instead of 4 all the same), different angles and the different lengths for the sides in place of a, but none of those options seemed to work.
I found one video online that was solving for the B at the center of a square loop. I believe the equation was 4*(4*pi*10^-7)*I*sin(theta)/(4*pi*a/2) where a was the length of the sides of the square. I was trying to use that with the rectangular wire by summing two versions of that equation, using 2 as the first coefficient for two sides at a time that were the same length (instead of 4 all the same), different angles and the different lengths for the sides in place of a, but none of those options seemed to work.