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
To find the value of the current flowing around the wire loop while the magnetic field is decreasing, we can use Faraday's law of electromagnetic induction, which states that the induced electromotive force (emf) in a wire loop is equal to the rate of change of magnetic flux through the loop.
The magnetic flux (Φ) through the loop can be calculated using the formula:
Φ = B * A * cosθ
Where:
B is the magnetic field strength (in Tesla),
A is the area of the loop (in square meters), and
θ is the angle between the magnetic field and the normal to the plane of the loop.
In this case, the angle θ is given as 30 degrees. The area of the loop can be calculated using the formula for the area of a circle:
A = π * r^2
Where:
r is the radius of the loop.
Let's calculate the area of the loop:
A = π * (0.10 m)^2
A = 0.0314 m^2
Now we can calculate the initial magnetic flux through the loop:
Φ1 = (6.0 x 10^−2 T) * (0.0314 m^2) * cos(30°)
Φ1 = 0.000942 T·m^2
The final magnetic flux through the loop is zero, as the magnetic field falls to zero.
The change in magnetic flux (ΔΦ) can be calculated by subtracting the initial magnetic flux from the final magnetic flux:
ΔΦ = 0 - 0.000942 T·m^2
ΔΦ = -0.000942 T·m^2
Next, we need to calculate the rate of change of magnetic flux (∆Φ/∆t). We are given that 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 rate of change of magnetic flux (∆Φ/∆t) can be calculated as:
∆Φ/∆t = (ΔΦ) / (Δt)
∆t = 2.0 seconds
∆Φ/∆t = -0.000942 T·m^2 / 2.0 s
∆Φ/∆t = -0.000471 T·m^2/s
Now, we can use Faraday's law of electromagnetic induction to calculate the induced electromotive force (emf):
emf = -N * (∆Φ/∆t)
Where:
N is the number of turns in the wire loop.
The number of turns (N) is not given in the question. Please provide the number of turns in the wire loop so we can calculate the emf and current flowing through the loop.
To find the value of the current flowing around the wire loop while the magnetic field is decreasing, we can use Faraday's Law of Electromagnetic Induction.
Faraday's Law states that the induced electromotive force (EMF) in a circuit is equal to the rate of change of magnetic flux through the circuit. Mathematically, it is represented as:
EMF = -dΦ/dt
Where EMF is the induced voltage, dΦ/dt is the rate of change of magnetic flux, and the negative sign indicates that the induced current opposes the change in magnetic field.
In this case, the magnetic field falls at a steady rate from 6.0 x 10^(-2) T to zero in 2.0 seconds. To calculate the rate of change of magnetic flux, we must first determine the initial and final magnetic flux through the wire loop.
The magnetic flux (Φ) through a circular loop of radius r and magnetic field B is given by:
Φ = B * A
Where A is the area of the loop. In this case, the loop has a radius of 0.10 m, so the initial flux through the loop is:
Φ_initial = (6.0 x 10^(-2) T) * π * (0.10 m)^2 = 0.0188 Tm^2
The final flux through the loop is zero since the magnetic field becomes zero.
Now, we can calculate the rate of change of magnetic flux:
dΦ/dt = (0 - 0.0188 Tm^2) / (2.0 s) = -0.0094 Tm^2/s
Using Faraday's Law, we know that the induced EMF is equal to the rate of change of flux:
EMF = -dΦ/dt = -(-0.0094 Tm^2/s) = 0.0094 V
To find the current flowing around the wire loop, we can use Ohm's Law, which states that the current (I) in a circuit is equal to the voltage (V) divided by the resistance (R):
I = V / R
In this case, the resistance of the wire loop is given as 2.0 x 10^(-3) ohms, so:
I = 0.0094 V / (2.0 x 10^(-3) ohms) = 4.7 A
Therefore, the value of the current flowing around the wire loop while the magnetic field is decreasing is 4.7 A, not 0.8 A.