1. Ampere’s Law PH 203 Professor Lee Carkner Lecture 17

2. Test 2 on Monday  Covers everything since last test through Wednesday  10 multiple choice (20 points)  4 problems (20 points each)  Equations and constants given  but not labeled  Bring calculator  No PDA’s, no cellphones, no sharing  Study  PAL’s  Notes  Homework

3. Currents and Magnetism   It is also true that moving charged particles produce magnetic fields   Serious magnetic fields are produced by currents  What is the magnitude and direction of these fields?

4. Magnetic Field from a Current in a Wire   Needle deflected tangentially to the wire cross section   How can we find the direction and magnitude of the B field for any situation?

5. Right Hand Rule Revisited  Grasp the wire with your thumb in the direction of the current and your curled fingers indicate the direction of the field 

6. Ampere’s Law  To find the magnitude of the B field we use Ampere’s law   The integral of the product of ds and B around the entire path is equal to  0 i  Where  0 = 4  X 10 -7 T m /A and is called the permeability of free space  ∫ B ds =  0 i  where i is the charge enclosed by the path

7. B Field for a Wire  ∫ B ds =  0 i or B ∫ ds =  0 i  Since B is the same everywhere around the circle  B 2  r =  0 i B =  0 i/2  r  Magnetic field a distance r from a long straight wire with current i

8. B Field within a Wire   e.g. within the wire  In this case the B field is still B =  0 i enc /2  r   If the total radius of the wire is R i enc = i(  r 2 /  R 2 )  B = (  0 ir)/(2  R 2 )

9. Force on Two Parallel Wires   The B field then will exert a force on the other wire B =  0 i/2  d F = BiL =  0 iiL/2  d  F = (  0 i 1 i 2 L)/(2  d)

10. Next Time  Read 29.5-29.6  Problems: Ch 29, P: 9, 28, 37, 42, 49

11. Consider a charged particle in a circular orbit in a magnetic field. If the charge on the particle is doubled, and the velocity of the particle is doubled, what happens to the radius of the orbit? A)¼ the original B)½ the original C)the radius stays the same D)2 times the original E)4 times the original

12. The force on a current-carrying wire in a magnetic field is strongest when, A)the current is parallel to the field lines B)the current is at a 30 degree angle to the field lines C)the current is at a 45 degree angle to the field lines D)the current is at a 60 degree angle to the field lines E)the current is perpendicular to the field lines

13. Consider a vector that stands straight out from the face of a loop of wire that carries a current. The magnetic torque on the loop will be greatest when, A)the vector is aligned with the magnetic field B)the vector is at a 30 degree angle to the magnetic field C)the vector is at a 45 degree angle to the magnetic field D)the vector is at a 60 degree angle to the magnetic field E)the vector is perpendicular to the magnetic field