Tuesday, April 6, 1999
Announcements:

Lecture notes:

•  A solenoid  is a tightly wound helical coil of wire. See figures 30-17 and 30-18 on page 738 of the text for a picture.
• The magnetic field outside of a solenoid is very, very small.

• To determine the magnitude of B inside the solenoid, draw an amperian loop as shown.
• I(integral) B (dot product) ds = I (integral from a to b) B (dot product) ds + I (integral from b to c) B (dot product) ds + I (integral from c to d) B (dot product) ds + I (integral from d to a) B (dot product) ds
• B = 0 outside of a solenoid, so I (integral from c to d) B (dot product) ds = 0
• I (integral from b to c) B (dot product) ds  =  I (integral from d to a) B (dot product) ds = 0 because the field is perpendicular to ds.
• B is only found inside the solenoid, so I(integral) B (dot product) ds = I (integral from a to b) B (dot product) ds  = m_o N i
• But, I (integral from a to b) B (dot product) ds = Bh
• Therefore, Bh =  m_o N i and B =  m_o N i/ h
• N/h = n = winding per length
• The magnetic field due to a coil is similar to the field due to a magnetic dipole (ie. a small magnet)
• 

• So far since the second midterm we have learned about .....
• current of a moving charge experiences a force in B
• current creates a magnetic fields
• We will now learn that a changing magnetic field ( or more accurately, changing B (dot product) A) induces current flow.

• In the first experiment, a galvonometer is connected to a coil and a magnet is brought near the coil.
• A galvonometer detects current flow when the magnet is moving
• Thus, if the magnet is stationary, there is no deflection in the galvonometer.
• If the north pole of the magnet is facing the loop,and the magnet is moving towards the loop, the deflection in the galvonometer is positive(to the right)
• The faster the motion, the larger the deflection.
• If the magnet is moving away from the loop, the direction of deflection is opposite that of when the magnet is moving towards the loop.
• If the south pole is facing the loop, and the magnet is moving towards the loop, the deflection is negative (to the left)
• If the magnet is moving along the plane of the loop, the deflection is much smaller than when it is perpendicular to the plane of the loop.
• Conclusion from experiment one: A changing magnetic field induces a current in a closed loop; more accurately a changing magnetic field induces an emf in the closed loop.

• Faraday's Law: x_induced = - dF/ dt, where F= I(integral) B (dot product) dA = magnetic flux
• If there are N loops in the coil,  x_induced = - N(dF/ dt)
• The magnitude of B can be thought to be proportional to the number of field lines per unit area; F= total number of lines passing a surface of area A

• At t= P, the switch in the first coil is closed allowing the B field due to the coil increase. Therefore, the number of field lines passing through the first coil (and hence the second coil) increases
• x_{in the second coil} = - dF/ dt = - d/dt (BAcosq)
• Direction of the induced emf; (Why is there a minus sign in x_induced = - dF/ dt)?
• Lenz's Law:  The direction of the induced current in a closed loop is such as to oppose the change that produces it or the direction of induced emf is such as to oppose the charge that produces it.