- #1

Zack K

- 166

- 6

- Homework Statement
- A thin coil is located at the origin; its radius is 5 cm and its axis lies on the##x##axis. It has 40 low-resistance turns and is connected to a 80 Ω resistor. A second thin coil is located at <15, 0, 0> cm and is traveling toward the origin with a speed of 8 m/s; it has 50 low-resistance turns, its axis lies on the axis, its radius is 4 cm, and it has a current of 17 A, powered by a battery. What is the magnitude of the current in the first coil?

EDIT: I managed to get the answer, but I'm not sure where the "mark solved" button is.

- Relevant Equations
- ##emf = -\frac {d\phi}{dt}##

##\frac {d\phi}{dt} = -\frac {dB}{dt}A##(A is the cross sectional area of the loop)

I will first calculate the magnetic flux of the coil in motion.

$$\frac {d\phi}{dt} = -\frac {dB_{loop}}{dt}A = -\frac{d}{dt}(\frac{\mu_o}{4\pi}\frac {2\pi NR^2I}{(R^2+z^2)^{\frac{3}{2}}})A$$differentiating in terms of ##z##, we get $$\frac {d\phi}{dt} =(\frac{\mu_o}{4\pi}\frac {6\pi^2 NR^4Iz}{(R^2+z^2)^{\frac{5}{2}}})\frac{dz}{dt}$$The area was just ##\pi R^2## and I just brought that into the expression. ##\frac{dz}{dt}## is our velocity.

Assuming this process is correct, I'm not sure on how to find the emf on the stationary coil. Is this expression for the coil in motion, or for the stationary coil? The distance term ##z## is making me think it's for the stationary coil, because why would a coils own change in flux have a distance term for it?

$$\frac {d\phi}{dt} = -\frac {dB_{loop}}{dt}A = -\frac{d}{dt}(\frac{\mu_o}{4\pi}\frac {2\pi NR^2I}{(R^2+z^2)^{\frac{3}{2}}})A$$differentiating in terms of ##z##, we get $$\frac {d\phi}{dt} =(\frac{\mu_o}{4\pi}\frac {6\pi^2 NR^4Iz}{(R^2+z^2)^{\frac{5}{2}}})\frac{dz}{dt}$$The area was just ##\pi R^2## and I just brought that into the expression. ##\frac{dz}{dt}## is our velocity.

Assuming this process is correct, I'm not sure on how to find the emf on the stationary coil. Is this expression for the coil in motion, or for the stationary coil? The distance term ##z## is making me think it's for the stationary coil, because why would a coils own change in flux have a distance term for it?

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