Would someone check this please?
A circular loop of wire of radius 0.10 m and of resistance 2.0 x 10^−3 ohms is in a region where there is a uniform magnetic field B.
The field is at 30deg to the normal to the plane of the wire loop as shown in Figure 3. The magnitude of the
magnetic field falls at a steady rate from 6.0 x 10^−2 T to zero in 2.0 seconds.
What is the value of the current flowing round the wire loop while the field is decreasing?
I get 0.8A
I = (induced emf)/R
Induced emf = (area)(dB/dt)* cos 30
dB/dt = 0.03 T/s
Area = (pi/4)R^2 = 7.85*10^-3 m^2
I do not agree with your answer
To find the value of the current flowing around the wire loop while the magnetic field is decreasing, you can use Faraday's law of electromagnetic induction.
According to Faraday's law, the induced electromotive force (emf) in a closed loop is equal to the rate of change of the magnetic flux passing through the loop. Mathematically, this can be expressed as:
emf = -dΦ/dt
Where emf is the induced electromotive force, dΦ/dt is the rate of change of magnetic flux, and the negative sign indicates that the induced current will oppose the change in magnetic field.
In this case, the magnitude of the magnetic field falls at a steady rate from 6.0 x 10^-2 T to zero in 2.0 seconds. The change in magnetic field can be calculated as:
ΔB = B_final - B_initial
ΔB = 0 - 6.0 x 10^-2 T
ΔB = -6.0 x 10^-2 T
The rate of change of magnetic flux is given by the product of the change in magnetic field and the area of the loop:
dΦ/dt = ΔB * A
The area of the circular loop can be calculated using the formula:
A = π * r^2
Where r is the radius of the loop. Substituting the values:
A = π * (0.10 m)^2
A = 0.0314 m^2
Now, we can calculate the rate of change of magnetic flux:
dΦ/dt = -6.0 x 10^-2 T * 0.0314 m^2
dΦ/dt = -1.884 x 10^-3 T * m^2
Finally, we can calculate the value of the current flowing around the wire loop using Ohm's law:
emf = -dΦ/dt = I * R
Where I is the current flowing through the wire loop and R is the resistance of the loop.
I = emf / R
I = (-1.884 x 10^-3 T * m^2) / (2.0 x 10^-3 ohms)
I = -0.942 A
Since the negative sign indicates that the current will oppose the change in magnetic field, the magnitude of the current flowing around the wire loop while the field is decreasing is 0.942 A.