A circular conducting coil with radius 3.40 cm is placed in a uniform magnetic field of 1.090 T with the plane of the coil perpendicular to the magnetic field. The coil is rotated 180° about the axis in 0.222 s.
(a) What is the average induced emf in the coil during this rotation?
I got 35.7mV and I am almost positive this is right.
(b) If the coil is made of copper with a diameter of 0.900 mm, what is the average current that flows through the coil during the rotation?
I used I=V/R and R=pL/A (where p is resistivity of copper 1.67e-8) and got I 481A but this is not right. Please help!
I agree, b is not even close.
I=.0357volts/R
R=1.67E-8*PI*.9EE-3/(.45EE-3)^2*PI
I=.0357*.45^2*E-6*PI/(1.67E-8PI*.9E-3)=480amps
Ok, checking A, something is wrong.
V=1/2 turn/.222sec*PI*.034^3*1.09= = 0.00030313086 volts. So recheck your EMF
I don't understand what you just did for A.
I used emf=change in flux/change in time
flux = magnetic field*area
according to my book, the answer for A is right. Please explain!
So just for the record, the answer for A is right.
For B, when calculating the resistance R, I messed up in regards to the radii. For the length i needed to use r=.034m and for the area r=4.5e-4m. What a silly mistake.
Cheers! and thanks for responding! :)
To solve the problem, we can use Faraday's law of electromagnetic induction, which states that the induced electromotive force (emf) in a circuit is equal to the rate of change of magnetic flux through the circuit.
(a) To find the average induced emf in the coil during rotation, we can calculate the change in magnetic flux. The magnetic flux through the coil can be calculated using the formula:
Φ = B * A * cos(theta)
Where:
Φ = Magnetic flux
B = Magnetic field strength
A = Area of the coil
theta = Angle between the magnetic field direction and the normal to the coil's plane
In this case, the magnetic field strength (B) is given as 1.090 T, and the radius of the circular coil (r) is given as 3.40 cm. So, the area of the coil (A) can be calculated as:
A = π * r^2
Now, since the plane of the coil is perpendicular to the magnetic field, the angle theta is 0 degrees, and the cosine of 0 degrees is 1. Therefore, the magnetic flux (Φ) is:
Φ = (1.090 T) * (π * (0.034 m)^2)
Next, to calculate the change in magnetic flux, we need to find the difference in the magnetic flux at the initial and final states. The coil is rotated 180°, which means the magnetic flux changes by twice the amount calculated above:
ΔΦ = 2 * Φ
Finally, we need to calculate the average induced emf (E). The average induced emf is given by:
E = ΔΦ / Δt
Where:
ΔΦ = Change in magnetic flux
Δt = Change in time
The time (Δt) is given as 0.222 s. Therefore, the average induced emf is:
E = (2 * Φ) / (0.222 s)
Calculating this value will give you the correct answer for part (a).
(b) Now, to find the average current that flows through the coil during the rotation, we can use Ohm's law, which states that the current (I) flowing through a resistor is equal to the voltage (V) across the resistor divided by its resistance (R).
In this case, the voltage across the coil is the induced emf (E) we calculated in part (a). And the resistance (R) of the coil can be calculated using the formula:
R = ρ * (L / A)
Where:
R = Resistance
ρ = Resistivity of copper (given as 1.67e-8 Ω·m)
L = Length of the coil (which is the same as the circumference of the coil)
A = Area of the coil (which we calculated earlier)
The length (L) can be calculated using the diameter (d) given as 0.900 mm:
L = π * d
Now, using the calculated values of E and R, you can plug them into the equation:
I = E / R
Calculating this expression will give you the correct answer for part (b).