Current Loops in a Magnetic Field Problem Question.

[R0B0]

Hi, I'm just wondering if anyone knows how I should be setting up my FBD for this question, or any hints as to how to go about doing this question:

"A long piece of wire with a mass of 0.100 kg and a total length of 4.00 m is used to make a square coil with a side of 0.100 m. The coil is hinged along a horizontal side, carries a 3.40 A current, and is placed in a vertical magnetic field with a magnitude of 0.0100T. Determine the angle that the plane of the coil makes with the vertical when the coil is in equilibrium. Find the torque acting on the coil due to the magnetic force at equilibrium".

I think I know how to do part b but I'm pretty sure that requires the angle from part A. I'm assuming you sum up your forces (FB and Gravity?) and solve for the angle but I'm just hung up on the fact that its hinged and I'm just having problems getting started.

Any help would be appreciated, thanks.

-Rob

 

[Nate810]

For part A, you can set up a free body diagram of the coil, with the hinge point being the pivot point. Draw an arrow pointing downwards for the gravitational force, and an arrow pointing outwards from the center of the coil to represent the magnetic force. Then you can use the equation F=ma to solve for the angle. For part B, you can then use the torque equation: τ = r × F, where r is the distance from the pivot point to the point of action of the force, and F is the magnetic force. You can solve for the torque at equilibrium, i.e. when the coil is in balance.

 

[wais]

ert

Hi Robert,

Setting up a free body diagram (FBD) is key to solving this problem. Here are some steps to help you get started:

1. Draw a diagram of the situation, including the wire, the square coil, and the magnetic field. Label all the given values and unknowns.

2. Identify all the forces acting on the coil. In this case, you have the weight of the coil (mg) pulling it downwards, and the magnetic force (FB) acting perpendicular to the current and the magnetic field.

3. Since the coil is hinged along a horizontal side, there will also be a normal force (FN) acting perpendicular to the surface of the hinge. This force will counteract the weight of the coil and keep it in equilibrium.

4. Draw arrows to represent the direction of each force. Remember that the magnetic force will be perpendicular to both the current and the magnetic field, and the normal force will be perpendicular to the surface of the hinge.

5. Write out the equations for each force. For the weight, it will be mg, for the magnetic force it will be FB = IBL (where I is the current, B is the magnetic field, and L is the length of the wire), and for the normal force it will be FN = mg.

6. Now, since the coil is in equilibrium, the sum of all the forces acting on it must be equal to zero. This means that you can set up an equation with all the forces and solve for the unknown angle.

7. Once you have the angle, you can use it to find the torque acting on the coil due to the magnetic force. Remember that torque is calculated by multiplying the force by the perpendicular distance from the pivot point. In this case, the pivot point is the hinge, and the perpendicular distance will be the length of the side of the coil.

I hope this helps you get started on solving the problem. Remember to always draw a clear and accurate FBD, and to carefully consider all the forces acting on an object before setting up your equations. Good luck!