Wed. Feb. 18 – Physics Lecture #30 Magnetic Fields 1. Magnetic Fields 2. Magnetic Moments & Torque 3. Ampere’s Law Warm-Up, Discuss with Neighbors: Wire 1 carries current I going up as shown. Wire 2 is a distance d away from wire 1, and carries current I going down as shown. Do the wires attract, repel, or something else? 1 2 d 1. Up 2. Down 3. Right 4. Left 5. Into page 6. Out of page 0. No direction/zero a)What is the direction of the magnetic field at the location of wire 2 due to the current in wire 1? b) What is the direction of the magnetic force acting on wire 2 due to the magnetic field from wire 1?

Magnetic Field of Special Current Configurations Axis of Loop of radius R, distance x from center: Direction: fingers along current; thumb along magnetic moment Center of Loop of radius R, so that x = 0 : Direction: fingers along current; thumb in field direction Center of Arc of radius R, angle  : Direction: fingers along current; thumb in field direction Axis of bar magnet with moment , distance x from center: Direction: magnetic moment from South pole to North pole Axis of long solenoid, away from edges, with n turns per meter: Direction: fingers along current; thumb in field direction Long (“infinite”) Straight Wire, distance r away from wire: Direction: thumb along current; fingers curl in field direction

What is the magnetic field (magnitude and direction) at the origin? Two long straight wires are the same distance 0.5 m from the origin. The wire on the y-axis has current 0.75 A going into the page. The wire on the x-axis has current 1 A coming out of the page.

A single piece of wire is bent so that it includes a circular loop of radius a, as shown. A current I flows in the direction indicated. Determine the magnetic field (magnitude and direction) at the center of the loop. I I I a

ConceptCheck: A square loop of wire with sides of length L carries a current I in a clock-wise direction; the current loop is in a uniform magnetic field B that is in the plane of the page and pointing to the right, as shown. a) What is the direction of the magnetic force acting on the right-most piece of loop? b) What is the direction of the net magnetic force acting on the entire loop? c) What is the direction of the net torque acting on the entire loop? (Take center of loop as reference point.) Assuming the loop started from rest, what would be its subsequent motion? 1. Up 2. Down 3. Right 4. Left 5. Into page 6. Out of page 0. No direction/zero

What is the equivalent magnetic moment (magnitude and direction) of this current loop? What is the torque (magnitude and direction) acting on the current loop? A current loop ( N = 10, A = 0.01 m 2, I = 1 A,) makes an angle of 30 o with a uniform magnetic field of magnitude 0.2 T directed to the right, as shown in the figure. Assume the current is going into the page at the lower left hand part of the loop and out of the page at the upper right hand part of the loop, as indicated on the sketch. 30 o

Gauss’s Law for Electricity? Gauss’s Law for Magnetism? Ampere’s Law?

A long conducting rod of radius R carries a non-uniform current density given by J = J 0 r / R, where J 0 is a constant and r is the radial distance from the axis of the rod. a) Use Ampere’s Law to determine the magnetic field strength outside the rod in terms of the enclosed current. b) Use integration to determine the enclosed current. c) Use Ampere’s Law to determine the magnetic field strength inside the rod.