Magnetism CHAPTER 29 Magnetic fields exert a force

Magnetism CHAPTER 29: Magnetic fields exert a force on moving charges. CHAPTER 30: Moving charges (currents) create magnetic fields. CHAPTERS 31, 32: Changing magnetic fields create electric fields. (Induction)

Magnetic fields • Magnetic poles, forces, and fields • Force on a moving charged particle • Force on a current-carrying wire

Magnets and Magnetic Forces Similar model to electrostatics: Each magnet has two poles at its ends. S N B is the magnetic field vector (magnetic flux density) Magnetic poles come in two types, “N” and “S”. Due to the Earth’s magnetism, a magnet will tend to rotate until the “N” end points North. (the earth’s north magnetic pole is actually a south pole) Forces between magnets are due to the forces between each pair of poles, similar to the electrostatic forces between point charges.

N N S S S unlike poles attract like poles repel N N N The force gets smaller as distance increases.

Magnetic Field B Magnetic poles produce a field B (think of S as a – charge and of N as a + charge) The external field exerts forces on poles N S F F N S B B

Quiz What is the direction of the force on a magnetic dipole placed in a uniform magnetic field? B S N

Magnetic field lines and Magnetic Dipoles Compass needle (a magnetic dipole) aligns with B B B compass N S S N Lines point out from N pole

Electric charge and Magnetic fields Hans Ørsted discovered (1819) that moving electric charges create magnetic fields. Also, external magnetic fields exert forces on moving electric charges. A current loop acts like a magnetic dipole.

Define B by the force that an external field exerts on a moving charge: Charge q moving with velocity , feels a force (vector product) F B q + v

1) 2) NO work done! 3) 4) For a negative charge, the force is in the opposite direction. UNITS: Also… 1 Gauss (G) = 10 -4 T

Typical Fields Earth’s Field ~ 1 x 10 -4 T (1 Gauss) Strong fridge magnet ~ 10 -2 T (100 G) Big lab electromagnet ~ 4 T (40, 000 G) Superconducting magnet up to ~ 20 T (200, 000 G)

Vector Diagrams The three vectors F, v, B never lie in a single plane, so the diagrams are always three-dimensional. The following convention helps with drawing the vectors. For vectors perpendicular to the page, we use: X into the page (tail feathers of arrow) out of the page (point of arrow)

Examples For a positive charge q moving with velocity v: draw the force vector. x x x x B x vx B v v x v B B

B Wire + + + + current I L Current I flows from left to right. In what direction is the force on the wire?

B + + + + The total force on the wire of length L is F = Nqv x B, where N is the number of charges in length L. N = (number of charges/volume) x (volume) = n x (AL), where A is the cross-sectional area So, F = (n. ALqv) x B = (nqv. A)L x B or, F=ILx. B (straight wire, uniform B) The vector length L points along the wire in the direction of the current.

Example Assume the earth’s magnetic field is 0. 5 x 10 -4 T, and points North, 50 o below the horizontal. up 0. 5 x 10 -4 T What is the force (magnitude and direction) on a straight horizontal power line 100 m long, carrying 400 A: A) if the current is flowing North B) if the current is flowing East north 50 o

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