A flat circular coil with 193 turns, a radius of 5.50 x 10-2 m, and a resistance of 0.241 Ω is exposed to an external magnetic field that is directed perpendicular to the plane of the coil. The magnitude of the external magnetic field is changing at a rate of ΔB/Δt = 0.908 T/s, thereby inducing a current in the coil. Find the magnitude of the magnetic field at the center of the coil that is produced by the induced current.
I did the following calculations, but still got the wrong answer. What am I doing wrong?
E=193(pi)(5.5E-2)^2(0.908)=1.6654
I=E/R=1.6654/0.241 ohms=6.9104 amps
B= (4pi E-7)(193) (6.9104) 2(5.5E-2)
B=1.8436 E-4
To find the magnitude of the magnetic field at the center of the coil that is produced by the induced current, you can use the formula for the magnetic field produced by a circular coil:
B = (μ₀ * N * I) / (2 * R)
Where:
- B is the magnetic field
- μ₀ is the permeability of free space, equal to 4π × 10^-7 T·m/A
- N is the number of turns in the coil
- I is the current flowing through the coil
- R is the radius of the coil
Based on your calculations, you correctly found the current flowing through the coil (I = 6.9104 A). Now, let's use this value along with the other given values to calculate the magnetic field.
Plugging in the values:
B = (4π × 10^-7 T·m/A) * (193 turns) * (6.9104 A) / (2 * 5.5 × 10^-2 m)
Simplifying the expression:
B = 1.8436 × 10^-4 T
It seems like you made an error in your calculation. The correct magnitude of the magnetic field at the center of the coil that is produced by the induced current is 1.8436 × 10^-4 T.