Magnetic field due to a solenoid

[musicmar]

Homework Statement

A 5-turn coil 1.0 cm in diameter is rotated at 10 rev/s about an axis perpendicular to a uniform magnetic field. A voltmeter connected to the coil through rotating contacts reads a peak value of 360 uV. What is the magnetic field strength?

The Attempt at a Solution

B=u₀nI
u₀= 8.85 x 10^-12 C²/N m²
n = 5

I'm not exactly sure how to find the current.

I know that the induced EMF = Blv, but I don't know what to do about length.
v=omega*r = 0.05 m/s

So, once I find either the length or the current, I should be able to find B.

 

[anathema]

Any help would be greatly appreciated!



Thank you for your question. In order to find the magnetic field strength, we need to use the equation B=u0nI, where u0 is the permeability constant, n is the number of turns in the coil, and I is the current flowing through the coil. In this case, we are given the values of u0 and n, so we just need to find the current.

To find the current, we can use the equation for induced EMF, which is given by EMF = Blv. In this equation, l represents the length of the coil, v is the velocity of rotation, and B is the magnetic field strength. Since the coil is rotating at 10 rev/s, we can calculate the velocity as v = 2πr = 0.05 m/s, where r is the radius of the coil.

Now, we can rearrange the equation for EMF to solve for I, which gives us I = EMF/(Blv). Plugging in the values we know, we get I = (360 uV)/(B*5*0.05 m/s). Since the units for EMF are in volts, we need to convert 360 uV to volts, which gives us 0.00036 V. Plugging this value in, we get I = (0.00036 V)/(B*5*0.05 m/s).

Finally, we can solve for B by rearranging the equation to B = (0.00036 V)/(I*5*0.05 m/s). Plugging in the value we found for I, we get B = (0.00036 V)/(0.00072 A*0.05 m/s) = 0.0012 T.

So, the magnetic field strength is 0.0012 Tesla. I hope this helps! Let me know if you have any further questions or need clarification on any of the steps. Good luck!