Ampere’s Law Physics 102 Professor Lee Carkner Lecture 19

PAL #18 Magnetic Force  How long would it take an electron to complete one circular orbit around a 1 G magnetic field?   Distance around circle is circumference: d = 2  r  Can find velocity from equation: r = mv/qB   t = (2  r)/(rqB/m) = 2  m/qB  t = [(2)(  )(9.1X )]/[(1.6X )(1X10 -4 )]  t =

Consider a charged particle in a circular orbit in a magnetic field. If the charge on 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

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

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

Currents and Magnetism  We saw how magnetic fields produce a force on a moving charged particle   A single moving particle produces only a small, fleeting field   What is the magnitude and direction of these fields?

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?

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 

Ampere’s Law  To find the magnitude of the B field we use Ampere’s law   The sum of the product of  L and B around the entire path is equal to  0 I  Where  0 = 4  X T m /A and is called the permeability of free space   B  L =  0 I

B Field for a Wire  Use Ampere’s law for a circle of radius r around the wire  B  L =  0 I or B   L =  0 I   However,   L around the whole circle is equal to the circumference = 2  r, so: B =  0 I/2  r  Magnetic field a distance r from a long straight wire with current I

Today’s PAL  Consider two parallel metal rails 1 cm apart and each carrying A of current in opposite directions  What is the direction and magnitude of B at a point halfway in-between them?  What is the direction and magnitude of the force on a conductor also carrying A that connects the two rails? I I

Force on Two Parallel Wires   The B field then will exert a force on the other wire F = BIL =  0 IIL/2  d  For two wires of equal length but different currents: F =  0 I 1 I 2 L/2  d

Magnetic Field: Loop   Can apply the right hand rule all the way around   Loop acts as a bar magnet

Magnetic Field: Solenoid  What happens if you stack several loops up?   You produce a solenoid   Field inside the solenoid is strong and uniform (far from the ends)

Electromagnet  We can write an expression for the solenoid magnetic field: B =  0 nI   If you put a piece of iron in the center you get an electromagnet 

Next Time  Exam #2  Same format as Exam #1  Covers chapters  Practice problems posted on WebAssign  Will not count for grade  Reading and homework for Monday on webpage