sUPPOSE YOU HAVE A square coil and a triangular coil each have sides of length L. The triangular coil has twice as many turns as the square coil. If a the same current is sent through each coil, when the coils are placed in the same uniform magnetic field making an angle of 30° with the planes of the coils, which coil experiences the greater torque?
It depends on the magnitude of the magnetic field that the coils are placed in.
2. Both coils experience the same torque.
3. the triangular coil
4. the square coil
To determine which coil experiences the greater torque, we need to consider the formula for torque experienced by a current-carrying coil in a magnetic field.
The formula for torque on a coil is given by the equation: Torque = NIA * B * sin(theta), where N is the number of turns in the coil, I is the current, A is the area of the coil, B is the magnetic field strength, and theta is the angle between the plane of the coil and the magnetic field.
In this case, both coils have the same current (I) running through them, and they are placed in the same uniform magnetic field at an angle of 30° (theta). We are given that the triangular coil has twice as many turns (N) as the square coil, and both have sides of length L.
To compare the torque experienced by each coil, we need to consider the area (A) of each coil. The area of the square coil is L^2, and the area of the triangular coil is 1/2 * L * L (since it's a right-angled triangle with base L and height L).
From the given information, we can conclude that:
1. The triangular coil has twice as many turns as the square coil (N_triangular = 2*N_square).
2. The current (I) is the same for both coils.
3. The angle between the plane of the coil and the magnetic field (theta) is 30° for both coils.
Now, if we substitute the values into the torque formula, we have:
For the square coil: Torque_square = N_square * I * A_square * B * sin(30°)
For the triangular coil: Torque_triangular = N_triangular * I * A_triangular * B * sin(30°)
Since N_triangular = 2 * N_square, the torque formula becomes:
Torque_triangular = 2 * N_square * I * A_triangular * B * sin(30°)
To compare the torques, we need to compare the areas of the coils:
A_square = L^2
A_triangular = 1/2 * L * L
If we substitute these values into the torque equations, we have:
Torque_square = N_square * I * L^2 * B * sin(30°)
Torque_triangular = 2 * N_square * I * (1/2 * L * L) * B * sin(30°)
Simplifying the expressions, we get:
Torque_square = N_square * I * L^2 * B * 1/2
Torque_triangular = N_square * I * L^2 * B * 1/2
Comparing the two torques, we can see that they are equal! So both the square coil and the triangular coil experience the same torque when placed in the same uniform magnetic field at an angle of 30° with the planes of the coils. Therefore, option 2 is correct: Both coils experience the same torque.