Average induced emf in coil

[kbyws37]

A circular conducting coil with radius 2.61 cm is placed in a uniform magnetic field of 0.827 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? (b) If the coil is made of copper (ρ = 1.67 times 10−8 Ω·m) with a diameter of 0.900 mm, what is the average current that flows through the coil during the rotation?



How would I start this problem?
I tried using Faraday's equation, but am getting the wrong answer
thanks

 

[hage567]

Show your work so we can see what you're doing.

 

[m2003]

To start this problem, you can use Faraday's law of induction, which states that the induced emf in a coil is equal to the negative rate of change of magnetic flux through the coil. In this case, the coil is rotated in a uniform magnetic field, so the magnetic flux through the coil will change as the coil rotates.

To solve part (a), you will first need to determine the magnetic flux through the coil. This can be calculated using the formula Φ = BAcosθ, where B is the magnetic field, A is the area of the coil, and θ is the angle between the magnetic field and the normal to the coil. In this case, θ is 90 degrees since the plane of the coil is perpendicular to the magnetic field.

Next, you will need to determine the change in flux during the rotation. Since the coil is rotated 180 degrees, the change in θ will be 180 degrees or π radians. You can then use the formula for average induced emf, which is ΔΦ/Δt, to calculate the average induced emf in the coil during the rotation.

For part (b), you can use Ohm's law (V = IR) to calculate the average current that flows through the coil. You will need to use the value of the average induced emf that you calculated in part (a) as the voltage (V) and the resistance of the copper coil (ρL/A) as the resistance (R), where ρ is the resistivity of copper, L is the length of the coil, and A is the cross-sectional area of the coil.