Magnetic Fields and Forces

AP Physics CMagnetic Fields and ForcesCurrents Set up Magnetic FieldsFirst Right-Hand Rule

Hans Christian Oersted(1777-1851)

Right-Hand Rule for Magnetic Fieldsx: into the page or away from you out of the page or towards you

Magnetic Field of a Current Loop:

Another look a Magnetic Fields of a Current Loop:

Electron as a Magnetic DipoleThe electron spins on its axis, givingrise to a electron current in thedirection of rotation.

The electron is like a magnetic dipole, a miniature magnet, with a north end and a south end.

Magnetic Spin Dipoles in Iron

Dual polarityCutting a magnet in halfwill not isolate a singlenorth or south. One magnet becomes two,then four, and so on. This process will never end; evenwhen the last electron spin dipole is reached, it cannot be cut to reveal a single north or single southpole.

Magnetic Fields of a Bar Magnet & the EarthB-field of bar magnet is similarto the Earth's magnetic field.B-field lines leave north face,enter at south face.Convection currents insidethe earth set up magnetic field.

Bar MagnetsIf magnetic dipole loops are oriented the sameon neighboring faces, the magnets attract.North is attracted to south,and is repelled by north.

Compass Needle is a Magnet: It Aligns with the B-Field

Magnetic Force on Current-Carrying Wire F = ILB sin

The direction of the force on the wire may be determined by a second right-hand rule, aright hand rule for magnetic force. The other right-hand rulegave the direction of themagnetic field B.

Using the Right-Hand RuleTo determine the direction of the magnetic force acting on the current-bearing wire

Using the RHR:In which direction, if any, will the metal rod be deflected?

Sample ProblemA wire 2.80 m in length carries a current of 5.00 A in a region where a uniform magnetic field has a magnitude of 0.390 T. Calculate the magnitude of the magnetic force on the wire if the angle between the magnetic field and the current is 60.0 degrees.Sample ProblemA thin, horizontal copper rod 1.0 m long and has a mass of 50 g. What is the minimum current in the rod that will cause it to float in a horizontal magnetic field that is perpendicular to the rod of 2.0 T?Torque on a Current LoopWhat is the net force on the current loop?What is the net torque on the loop?

Torque on the Current LoopAt what angle is the torque a maximum value?

At what angle is the torque a minimum value?Sample ProblemA circular loop of radius 2.0 cm contains 50 turns of tightly wound wire. If the current in the windings is 0.30 A and a constant magnetic field of 0.20 T makes an angle of 25 degrees with a vector perpendicular with the loop, what torque acts on the loop?DC Motor

Moving Charges in a B-Field:Electric force can be parallel to direction of velocity, but themagnetic force is always perpendicular to the velocity vector.

Magnetic Force on Moving ChargesRHRF = qvB sin

Magnetic Force on Moving ChargesIf the velocity v is parallel to the magnetic field B, the magnetic force is zero because sin = 0.

Magnetic Force on Moving ChargesWhat is the direction of the magnetic force on the moving charge in each situation?

Magnetic Force on Moving ChargesWhat is the direction of the force F , if any, in each case?

Charges move in a circular path:

Circular Paths in Magnetic Fields

Circular Motion in B-FieldRight Hand Rule for Force Fingers point in direction of magnetic field B.

Thumb points in direction ofthe velocity vector v. Palm shows the direction of the force F.

Mass SpectrometerF = qvB sin = 90 deg F = qvB F = ma a = v2 /r F = mv2 /r

qvB = mv2 /r m = qBr/v

Sample ProblemA singly charged positive ion moving at 4.6 x 105 m/s leaves a circular track of radius 7.94 mm along a direction perpendicular to the 1.80 T magnetic field of a bubble chamber. Compute the mass (in amus) of this ion, and identify it from that value.Velocity Selector & Mass SpectrometerIn the velocity selector, the E-force and the B-force are equal and opposite, so that, qE = qvB. Therefore, v = E/B.In 1897, J. J. Thomson used this set-up to determine the mass to charge ratio for electrons.

Sample ProblemThe electric field between the plates of a velocity selector is 2500 V/m, and the magnetic field in both the velocity selector and the deflection chamber has a magnitude of 0.0350 T. Calculate the radius of the path of a singly charged ion have a mass of 2.18 x 10-28 kg.Electron Beam in a B-FieldElectrons are deflected downward. What is the direction of the magnetic field B?

Magnetic FluxMagnetic flux is the product of the average magnetic field times the perpendicular area that it penetrates.

Magnetic Flux IllustrationsThe contribution to magnetic flux for a given area is equal to the area times the component of magnetic field perpendicular to the area. For a closed surface, the sum of magnetic flux is always equal to zero (Gauss' law for magnetism).

Gausss Law for MagnetismThe net magnetic flux out of any closed surface is zero. This amounts to a statement about the sources of magnetic field. For a magnetic dipole, any closed surface the magnetic flux directed inward toward the south pole will equal the flux outward from the north pole. The net flux will always be zero for dipole sources.

Sample ProblemA cube of edge length 2.50 cm is positioned so that it is position with one corner at the origin, one face in the xy-plane, one face in the yz-plane and one in the xz-plane. A uniform magnetic field given by B = (5.00i +4.00j +3.00k) T exists throughout the region.Calculate the flux through the face that is parallel to the yz-plane.What is the total flux through the six faces?