Tuesday, March 30, 1999
Announcements: None

Lecture notes:

•  We said the net force on a current loop in a constant magnetic field is zero, but the torque is not necessarily zero!
• F = i (L (cross product) B)
• Case One
• 
•  Net Force = 0      Net Torque = 0        t = r (cross) F
• Case Two
• 
• Net Force = 0         Net Torque does not equal zero
• Define axis of rotation:
• through ED, then t = (a) (i) (b) B
• If Area of loop = A = ab, then t = (a) (i) (b) B = i AB
• Through OF,  t = (1/2)(a) (i) (b) B + (1/2)a i b B = i AB
• 
• Resolve B into 2 components
• Bsinq perpendicular to normal
• Bcosq along the normal (no torque)
• The component of B that's perpendicular to normal ( in the Bsinq plane of the loop) gives the force
• F = i b Bsinq
• t = i b Bsinqa  = iABsinq = i(A (cross product) B)
• It is convenient to define a vector quantity for the area of the loop
• Area vector points along the normal of the loop
• To find direction use Right Hand Rule; Curl fingers in direction of i, thumb points in direction of A
• We have shown that for a current flowing around a rectangular loop, into a uniform B, the torque on the loop is              t = i(A (cross product) B),
• It can be shown that the above relation is correct for current loop of any shape.

• t  = i(A (cross product) B) = -Kq, where K is the spring constant and q is the angle of rotation

• The torque due to the current in the magnetic field is equal to the torque of the restoring spring.
• Read about Magnetic Dipoles on your own\

• We learned that magnetic field can exert a force on a moving charge or on a wire carrying a current.
• Moving charges or current are also sources of magnetic fields.
• Biot and Savart were the first to provide a quantitative description on how a current produces an electric field.

• q is the angle between i ds and r
• r is the displacement vector from ds to point P ; r is the unit vector
• dB is the magnetic field at point P due to the current element i ds
• dB = (m_o/4p) ( i ds (cross) r/ r²)
• (m_o/4p) = 10^-7 Tm/A
• m_o= permeability constant
• See example 30-1 on page 732 of the text.