The 2-cm (radius) current loop shown in the figure is changing from θ1 = 11 degrees to θ2 = 66 degrees in a magnetic field 2 T in 0.5 seconds. What is the magnitude of the induced emf to the nearest hundredth of a millivolt?

The wire in Problem 2 has a thickness of 1.04 mm and a resistivity of 1.71 x 10-8 Ωm. To the nearest tenth of a milliamp what is the induced current in the loop

Calcuate the change in magnetic flux and divide it by the time interval. That will give you the average EMF.
V = (change in BA cos theta)/0.5 s
B = 2 T
A = pi R^2 (with R in meters)
This assumes that "theta" is measured between the B field direction and the normal to the loop.

For the last part, compute the resistance of the wire
R = resisitivity* 2 pi R/A
since resisistivity is in ohm-cn, A must be in cm^2 and R in cm

I = V/R

To calculate the magnitude of the induced emf, we need to follow these steps:

Step 1: Calculate the change in magnetic flux (ΔΦ).
To calculate the change in magnetic flux, we use the formula:
ΔΦ = B * ΔA * cos(θ)
where B is the magnetic field (given as 2 T), ΔA is the change in area, and θ is the angle between the magnetic field direction and the normal to the loop.

Given that the loop is a circular loop with a radius of 2 cm, we can calculate the change in area (ΔA) as follows:
ΔA = π * (R2^2 - R1^2)
where R2 = radius when θ = 66 degrees, and R1 = radius when θ = 11 degrees.

Step 2: Convert the change in area to square meters.
Since the radius is given in centimeters, we need to convert it to meters by dividing by 100 (since 1 meter = 100 cm).

Step 3: Calculate the change in magnetic flux (ΔΦ) in Weber (Wb).
ΔΦ = B * ΔA * cos(θ)

Step 4: Calculate the average emf (V_average) by dividing the change in magnetic flux by the time interval.
V_average = ΔΦ / Δt
where Δt is the time interval given as 0.5 seconds.

Step 5: Convert the average emf to millivolts by multiplying by 1000.
V_millivolts = V_average * 1000

To calculate the induced current in the loop, we need to follow these steps:

Step 1: Calculate the resistance of the wire (R) using the formula:
R = resistivity * (2 * π * R) / A
where resistivity is given as 1.71 x 10^-8 Ωm, R is the radius in centimeters, π is a mathematical constant, and A is the cross-sectional area.

Step 2: Convert the radius to meters by dividing by 100.

Step 3: Convert the cross-sectional area to square centimeters by multiplying by 100.

Step 4: Calculate the induced current (I) using Ohm's law:
I = V_average / R

Step 5: Convert the induced current to milliamperes by multiplying by 1000.