1. Physics 152 Magnetism Walker, Chapter 22

2. 2 B Field Outside a Wire Earlier we said that magnetic fields are created by moving charges. A current in a wire, therefore, must create a magnetic field. Unlike the Electric field from a line of charges, the magnetic field generated by a current in a straight wire cannot be radial (outward).

3. 3 Magnetic Field from a Wire The magnetic field lines from a current form circles around a straight wire with the direction given by another “right hand rule” (thumb in direction of current, finger curl around current indicating direction of magnetic field).   r

4. 4 Question: Magnetic Field Direction What is the direction of the magnetic field at the point p created by the current I? 1.Into the screen 2.Up on the screen 3.Out of the screen 4.Down on the screen. p I

5. 5 Force on parallel wires Each of two parallel wires with current I, experiences an attractive magnetic force that diminishes as one over the distance separating the wires: F  I 1 I 2 L / d. d I1I1 I2I2

6. 6 Definition of Ampere The ampere (A) is defined such that two parallel wires separated by 1.0m and each carrying 1.00 A of current experience a force of attraction of 210 -7 N on each 1.00 m length of wire. This defines   = 4  x 10 -7 N / A 2   = Permeability of free space. d  

7. 7 Ampère’s Theorem Consider any closed loop in space –Doesn’t have to be a circle, or lie flat. –The sum (over all segments of the loop) of the product of the component of Magnetic field parallel to the loop times the length of the loop segment is equal to the product of  0 times the current enclosed by the loop.

8. 8 Ampere’s Law and a straight wire We already argued that the B-field generated by a wire has to form circles around the wire. Apply Ampere’s law

9. 9 Solenoids If we stack several current loops together we end up with a solenoid: In the limit of a very long solenoid, the magnetic field inside is very uniform: B=  0 n I n = number of windings per unit length, I = current in windings B  0 outside windings

10. 10 a) b) c) d) I1I1 I2I2 Question