F I l B In general for all wires in magnetic fields - PowerPoint PPT Presentation

Force on a Loop • In a uniform magnetic field a straight wire experiences a force.       F I l B • In general for all wires in magnetic fields    dF I dl B • For a uniform magnetic field only the displacement from the starting point to the ending point affects the magnetic force. 1 Spring 2004 OSU Magnetism Chapter 27

Force on a Loop Practice Problem (Similar to New HMWK Assignment) What is the force on a semicircle shaped loop, if the straight portion has a force of 10N on it? 1) 31.4 N 4) 15.2 N 2) 10 N 5) 5 N 3) 0 2 Spring 2004 OSU Magnetism Chapter 32

Force on a Loop Practice Problem (Similar to New HMWK Assignment) What is the current in the loop if the radius of curvature is 0.50m and the magnetic field is 4 T? 1) 2.5 A 3) 8.2 A 2) 1.25 A 4) 0 3 Spring 2004 OSU Magnetism Chapter 27

Torque on a Loop • Recall     b       r F F I dl B a • For a uniform field to the current     B F I l B  • then for a force arm F 2a to the magnetic force     2 aIlB ( 2 al ) IB AIB F       I A B 4 Spring 2004 OSU Magnetism Chapter 27

Torque on an Electric Dipole • Recall          r F F q E • then       q r E F q+ q - 2a F E 5 Spring 2004 OSU Magnetism Chapter 27

Magnetic Dipole Moments • Magnetic dipole Moment             I A B • Electric Dipole Moment         ˆ p E p 2 aq r ˆ r is a unit vector pointing from the negative to the positive charge 6 Spring 2004 OSU Magnetism Chapter 27

Torque on a Loop Practice Problem (From New HMWK Set) A square loop of side 0.3 m, B carries a current of 2 A. It is I placed inside a magnetic field of 0.05T. The left side of the loop is fixed. If the loop is parallel to B, what is the torque on the loop about the fixed axis? 1) 0.009 N.m 3) 0.003 N.m Fixed 2) 0.018 N.m 7 Spring 2004 OSU Magnetism Chapter 27

Charge Moving in a Magnetic Field  • component of velocity will cause circular motion. • Magnetic Force on the Charge provides the Centripetal Force 2 v   m F qvB r v mv r  r qB Cyclotron Frequency v  qB   r m B 8 Spring 2004 OSU Magnetism Chapter 27

Special Case of Lorentz Force • Lorentz Force        E F q E q v B • When F = 0 and B      v E B p + then E v  B 9 Spring 2004 OSU Magnetism Chapter 27

Hall Effect The magnetic force causes charge separation which e H shows up as a voltage difference. The E- field + + + + exerts a force on the - - - - charge that balances l Magnetic Force. E    H eE qv B v H d d B And the Hall Voltage is H H d   E l v Bl e 10 Spring 2004 OSU Magnetism Chapter 27

Hall Probe • Hall probes are used to measure the strength of magnetic fields. • They are used to measure the charge carrier concentration (from measuring the drift velocity). • Hall Probes are small and accurate. • They are used to determine the sign of charge. 11 Spring 2004 OSU Magnetism Chapter 27

Mass Spectrometer • When the velocity is known, then the mass is known by the charge and radius of curvature in a B field. 2 v  qvB m r mv r  qB p + B E 12 Spring 2004 OSU Magnetism Chapter 27

2 v  qvB m r 13 Spring 2004 OSU Magnetism Chapter 27