Ph126 Spring 2008 Lecture #8 Magnetic Fields Produced by Moving Charges

1. Ph126 Spring 2008Lecture #8Magnetic Fields Produced by Moving Charges Prof. Gregory Tarlé gtarle@umich.edu

2. Last Lecture: Magnetic Forces • Moving charges can experience forces in magnetic fields: • Magnitude: • Direction: Right-Hand Rule • Magnetic force does no work on the moving charge • Measure magnetic field in Tesla (T)

3. Electric vs. Magnetic Forces • The electric force is always in the direction of the electric field, but the magnetic force is always perpendicular to the magnetic field • The electric force acts on a charged particle independent of the particle’s velocity, but the magnetic force acts on a charged particle only when it is in motion • The electric force can change the speed of a charged particle while the magnetic force associated with a steady magnetic field changes the direction of the particle, but not its speed

4. Magnetic Field B Current I Concept Test #1 What direction is the force this wire feels because of the magnetic field? • To the right • To the left • Up the page • Down the page • Into the page • Out of the page

5. Magnetic Force on a Current angle between I and B

6. Torque on a Current-Carrying Coil The two forces on the loop have equal magnitude but they are opposite in direction.

7. Concept Test #2 A square loop carries a current I and pivots without friction about the z-axis. A uniform magnetic field B points in the +x direction, and the loop initially makes an angle θ with the x-z plane. The torque on the loop is clockwise. • True (yes) • False (no)

8. N = number of turns of wire Calculate the Torque

9. Max and Min Torques The loop tends to rotate such that its normal becomes aligned with the magnetic field

10. Origins of Magnetic Fields • Magnetic fields come from: • Magnets • Moving charges (i.e. currents) • Changing E fields (more next lecture…) • Magnetic field lines never end; they must form closed loops • No magnetic charges (monopoles) exist

11. B produced by a long straight wire Increases with current, falls off with distance permeability of free space

12. Direction of B field of a straight wire • The magnetic field due to the current in a long straight wire has circular field lines around the wire • The direction of the field is given by the right hand rule

13. P I r F I L Concept Test #3 Two identical parallel long straight wires carrying a current I stand a distance r apart. Which of the following statements is false? • The magnetic field B created by the bottom wire at P points out of the page. • The force exerted by the bottom wire on the top wire is F = ILB. • The force pushes the top wire up.

14. P I r F 2I L Concept Test #4 Two parallel long straight wires carrying currents I and 2I stand a distance r apart. Which of the following statements is false? • The magnetic force pulls the top wire down toward the bottom wire. • The magnetic force pulls the bottom wire up toward the top wire. • The magnetic force on the top wire is greater than the magnetic force on the bottom wire. The force is attractive if the currents are in the same direction and repulsive otherwise the two wires generate magnetic fields that pull one another toward each other  Newton’s 3rd Law.

15. Current flowing in a loop of wire creates a magnetic field Current loop can be imagined to be a phantom bar magnet Electromagnet = http://www.windows.ucar.edu/spaceweather/info_mag_fields.html

16. N At center of circular loop S Which side is north pole? • Right hand rule number of turns

17. Interior of a solenoid B produced by a solenoid number of turns per unit length

18. Ampere’s Law • Ampere’s law relates sum of B field along a line to current inside • Formally: net current passing through surface bounded by path

19. Same as before! B field of wire from Ampere’s Law

20. =

21. N S