5. Magnetic forces on current l A – drift velocity N – number of charge carriers in the volume lA n – density of charge carriers (in metals it is density of electrons) Example: A straight wire carrying a current is placed in a region containing a magnetic field. The current flows in the +x direction. There are no magnetic forces acting on the wire. What is the direction of the magnetic field?

Example 1: A horizontal wire carries a current and is in a vertical magnetic field. What is the direction of the force on the wire? 1) left 2) right 3) zero 4) into the page 5) out of the page B I Example 2: A vertical wire carries a current and is in a vertical magnetic field. What is the direction of the force on the wire? B I 1) left 2) right 3) zero 4) into the page 5) out of the page Example 3: A 1.5-m length of wire carrying 4.0 A of current is oriented horizontally. At that point, the Earth’s magnetic field is 5.0x10-5 T, and the dip angle is 30° to the wire. Estimate the magnitude of the magnetic force on the wire due to the Earth’s magnetic field of at this point. (The dip angle is the angle between the Earth’s magnetic field and the current in the wire. )

This is how a motor works !! 6. Current loop in magnetic field Example 1: A rectangular current loop is in a uniform magnetic field. What is the direction of the net force on the loop? B x z y 1) + x 2) + y 3) zero 4) - x 5) - y Using the right-hand rule, we find that each of the four wire segments will experience a force outwards from the center of the loop. Thus, the forces of the opposing segments cancel, so the net force is zero. Example 2: A wire loop is in a uniform magnetic field. Current flows in the wire loop, as shown. What does the loop do? 1) moves to the right 2) moves up 3) remains motionless 4) rotates 5) moves out of the page There is no magnetic force on the top and bottom legs, since they are parallel to the B field. However, the magnetic force on the right side is into the page, and the magnetic force on the left side is out of the page. Therefore, the entire loop will tend to rotate. This is how a motor works !!

Example: If there is a current in the loop in the direction shown, the loop will: 1) move up 2) move down 3) rotate clockwise 4) rotate counterclockwise 5) both rotate and move F N S N S B F B field out of North B field into South At the North Pole, the magnetic field points to the right and the current points out of the page. The right-hand rule says that the force must point up. At the south pole, the same logic leads to a downward force. Thus the loop rotates clockwise.

Wire and Loop with Electric Current in Magnetic Field Battery Axis of rotation Magnetic field Loop The loop will rotate (clockwise)

a b 6a. Current loop and magnetic moment Definition of magnetic dipole moment: b N – number of loops in the coil b

Example 1 : A current-caring circular coil is in uniform magnetic field. The maximum magnitude of the torque on the coil occurs when the angle between the field and magnetic moment is 0 45° 90° 135° 180° Example 2: A coil is oriented initially with its magnetic dipole moment antiparallel to a uniform magnetic field. In this orientation torque  is equal to: A)  = 0 B)  = max C) 0<  < max This is unstable equilibrium

Example: