A toroid is a solenoid in the shape of a donut. The magnetic field inside the toroid is B=μ0NI/(2πR).
Suppose that a toroidal electromagnet with 146 loops uses a coil 1.2 m in diameter made from square copper wire. The power supply produces 120 V at a maximum power output of 4.0 kW.
If P=IV, what is the magnetic field strength inside the coil?
To find the magnetic field strength inside the coil, we can use the equation B = μ₀NI / (2πR), where B is the magnetic field strength, μ₀ is the permeability of free space, N is the number of loops in the coil, I is the current flowing through the coil, and R is the radius of the coil.
Given:
Number of loops, N = 146
Radius of the coil, R = 1.2 m
Voltage, V = 120 V
Maximum power output, P = 4.0 kW
First, let's calculate the current flowing through the coil using the power formula P = IV.
P = IV
4.0 kW = I * 120 V
I = 4000 W / 120 V
I ≈ 33.33 A
Now we can substitute the values into the equation B = μ₀NI / (2πR).
B = (4π × 10^-7 T·m/A) * (146 loops) * (33.33 A) / (2π * 1.2 m)
Simplifying this expression:
B = (4π × 10^-7 T·m/A) * (146 * 33.33 A) / (2π * 1.2 m)
B = (4π × 10^-7 T·m/A) * (4853.18 A) / (2π * 1.2 m)
B = (4π × 10^-7 T·m/A) * (4044.32 A·m) / (2π * 1.2 m)
B ≈ 5.366 T
Therefore, the magnetic field strength inside the coil is approximately 5.366 Tesla.