# Magnetism Lab - University of Michigan

Ph126 Spring 2008 Lecture #8 Magnetic Fields Produced by Moving Charges Prof. Gregory Tarl [email protected] Last Lecture: Magnetic Forces Moving charges can experience forces in magnetic fields: Magnitude: F q vB sin

Direction: Right-Hand Rule Magnetic force does no work on the moving charge Measure magnetic field in Tesla (T) Electric vs. Magnetic Forces

The electric force is always in the direction of the electric field, but the magnetic force is always perpendicular to the magnetic field The electric force acts on a charged particle independent of the particles velocity, but the magnetic force acts on a charged particle only when it is in motion The electric force can change the speed of a charged particle while the magnetic force associated with a steady magnetic field changes the direction of the particle, but not its speed Concept Test #1 What direction is the force this wire feels

because of the magnetic field? Magnetic Field B 1) 2) 3) 4) 5) 6) To the right To the left Up the page Down the page Into the page Out of the page

Current I Magnetic Force on a Current F qvB sin q F vt B sin t L I F ILB sin angle between I and B Torque on a CurrentCarrying Coil

The two forces on the loop have equal magnitude but they are opposite in direction. Concept Test #2 A square loop carries a current I and pivots without friction about the z-axis. A uniform magnetic field B points in the +x direction, and the loop initially makes an angle with the x-z plane. The torque on the loop is clockwise. True (yes) False (no) Calculate the Torque

Recall : Fr sin clockwise " " Direction : counterclockwise "" 1 ILB 2 w sin ILB 12 w sin IAB sin magnetic moment

NIA B sin N = number of turns of wire Max and Min Torques The loop tends to rotate such that its normal becomes aligned with the magnetic field Origins of Magnetic Fields Magnetic fields come from: Magnets Moving charges (i.e. currents)

Changing E fields (more next lecture) Magnetic field lines never end; they must form closed loops No magnetic charges (monopoles) exist B produced by a long straight wire o I B 2 r 7

Increases with current, falls off with distance o 4 10 T m A permeability of free space Direction of B field of a straight wire The magnetic field due to the current in a long straight wire has circular field

lines around the wire The direction of the field is given by the right hand rule o I BP 2 r Concept Test #3 Two identical parallel long straight wires carrying a current I stand a distance r apart. Which of the following statements is false?

1) 2) 3) The magnetic field B created by the bottom wire at P points out of the page. The force exerted by the bottom wire on the top wire is F = ILB. The force pushes the top wire F up. P

I F r I L o I L o I 2 IL 2 r 2 r Concept Test #4 Two parallel long straight wires carrying currents I and 2I stand a

distance r apart. Which of the following statements is false? 1) 2) 3) The magnetic force pulls the top wire down toward the bottom wire. The magnetic force pulls the bottom wire up toward the top wire. The magnetic force on the top wire is greater than the magnetic force on the bottom

wire. F1 2 2 L o I 2 2 r P I F r 2I L

The force is attractive if the currents are in the same direction and repulsive otherwise the two wires generate magnetic fields that pull one another toward each other Newtons 3rd Law. Electromagnet Current flowing in a loop of wire creates a magnetic field Current loop can be imagined to be a phantom bar magnet

= http://www.windows.ucar.edu/spaceweather/info_mag_fields.htm Which side is north pole? Right hand rule N number of turns o I B N 2R

S At center of circular loop B produced by a solenoid Interior of a solenoid B o nI number of turns per unit length Amperes Law

Amperes law relates sum of B field along a line to current inside Formally: B I || o net current passing through surface bounded by path

B field of wire from Amperes Law B I || o B o I B 2 r o I o I B 2 r Same as before!

= N S

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