A wire has a length of 4.52 x 10-2 m and is used to make a circular coil of one turn. There is a current of 7.94 A in the wire. In the presence of a 8.04-T magnetic field, what is the maximum torque that this coil can experience?
The magnitude of torque is M=p•B•sinα,
where p is the magnetic moment, B is magnetic field.
Max M=p•B.
p=I•A, where A is the area of the loop.
If the length of the wire is L=2πR, the radius is R=L/2π,
the area is A= πR^2=L^2/4 π=1.626•10-4 (m^2)
Max M= I•( L^2/4 π) •B= 7.94•1.626•10-4•8.04=0.01 N•m
To calculate the maximum torque that this coil can experience, we need to use the formula for torque in a magnetic field. The formula for torque is given by:
Torque = magnetic moment x magnetic field
To find the magnetic moment of the coil, we can use the formula:
Magnetic moment = current x area
To find the area of the coil, we need to know the radius. We can calculate the radius of the coil using the length of the wire. The formula to calculate the radius of a coil is:
Radius = length / (2π)
Let's calculate the radius first:
Radius = 4.52 x 10^(-2) m / (2π) ≈ 0.00719 m
Now we can calculate the area of the coil using the formula for the area of a circle:
Area = π x (radius)^2
Area = π x (0.00719 m)^2 ≈ 0.000163 m^2
Next, we can calculate the magnetic moment of the coil using the formula:
Magnetic moment = current x area
Magnetic moment = 7.94 A x 0.000163 m^2 ≈ 0.001294 A.m^2
Finally, we can calculate the maximum torque by multiplying the magnetic moment by the magnetic field:
Torque = magnetic moment x magnetic field
Torque = 0.001294 A.m^2 x 8.04 T ≈ 0.0104 N.m
Therefore, the maximum torque that this coil can experience is approximately 0.0104 N.m.