1. What would the loop do in this situation? The loop will rotate about an axis halfway between the left and right sides of the circuit, parallel to the plane of the loop and perpendicular to the direction of the magnetic field. Axis of rotation The magnetic force causes a torque on the loop. 1 1 Angle between r and F is 90 o Angle between L and B is 90 o Torque due to force applied to one side of the circuit. Total torque on circuit. Notice that the torque on the loop depends on the current through the circuit, the magnetic field strength, and the area of the loop. Area of the loop

2. We can therefore write a more general expression for the torque on a current carrying loop in terms of the loop area. This is only valid for a current carrying loop placed in an external magnetic field. Remember that the area vector is always perpendicular to the plane containing the area. The Magnetic Dipole Moment determines how easy it is to rotate a current carrying loop in a magnetic field.  – Magnetic dipole moment (or magnetic moment) [Am 2 ] We are essentially looking at how direction of the external magnetic field and the direction of the magnetic field generated by the current in the wire are oriented relative to each other. If they are parallel there will be no torque, but anything other than parallel will cause a torque to try to align the two magnetic fields. The magnetic moment is a vector, whose direction is the same as the area vector. To determine this direction we use a second right-hand rule. 1. Curl your fingers in the direction that the current flows in the loop. 2. Thumb will point in the direction of the magnetic moment. i.This is also the direction of the magnetic field caused by the current that passes through the center of the loop.

3. The description of the magnetic dipole moment is identical to the description of the electric dipole moment. Torque due to magnetic dipole moment Torque due to electric dipole moment We can also look at the magnetic potential energy for a current carrying loop in an external magnetic field. When  and B are parallel: When  and B are perpendicular: When  and B are anti-parallel: U is a minimum U is a maximum Energy is released Energy is stored Assuming L is in z-dir, B is in x-dir and therefore the (constant) force is in the y-dir. If L is in z-dir and y is in y-dir the area must be in the x-dir.

4. We know that any charged particle moving at a specified velocity in an external magnetic field will travel in a circular path if it remains in that field for a long time. The radius of the path is determined by how fast the charge is moving as well as the strength of the magnetic field. How would we determine the radius of the path using these quantities? 1 The magnetic force causes the charge to move in a circular path. What do we call a force that pushes an object towards the center of a circular path? Centripetal Force Centripetal acceleration The magnetic force acts as a centripetal force. Radius of the path followed by a charged particle moving in an external magnetic field.

5. We can also look at the angular speed of the charge as it moves in its circular path. This is called the Cyclotron frequency Similarly we can determine the time it takes to complete one revolution or the period. Similarly, Distance traveled – circumference of the path Period – time to complete one revolution.

6. A rectangular loop is placed in a uniform magnetic field with the plane of the loop perpendicular to the direction of the field. If a current is made to flow through the loop in the sense shown by the arrows, the field exerts on the loop: 1. a net force. 2. a net torque. 3. a net force and a net torque. 4. neither a net force nor a net torque.

7. A rectangular loop is placed in a uniform magnetic field with the plane of the loop parallel to the direction of the field. If a current is made to flow through the loop in the sense shown by the arrows, the field exerts on the loop: 1. a net force. 2. a net torque. 3. a net force and a net torque. 4. neither a net force nor a net torque.

8. Two identical coils, as seen in the photographs below, are wired such that when the switch is pressed electric current will flow in the same direction around both coils. When the switch is pressed, producing current in the same direction in the coils, the coils will: (1) move away from each other. (2) move toward each other. (3) remain at rest.