Another look a Magnetic Fields of a Current Loop:
Electron as a Magnetic Dipole The electron spins on its axis, giving rise to a electron current in the direction of rotation. The electron is like a magnetic dipole, a miniature magnet, with a north end and a south end.
Dual polarity Cutting a magnet in half will not isolate a single north or south. One magnet becomes two, then four, and so on. This process will never end; even when the last electron spin dipole is reached, it cannot be cut to reveal a single north or single south pole.
Magnetic Fields of a Bar Magnet & the Earth B-field of bar magnet is similar to the Earth's magnetic field. B-field lines leave north face, enter at south face. Convection currents inside the earth set up magnetic field.
Bar Magnets If magnetic dipole loops are oriented the same on 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 θ The direction of the force on the wire may be determined by a second right-hand rule, a right hand rule for magnetic force. The other right-hand rule gave the direction of the magnetic field B.
Using the Right-Hand Rule To 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 Problem A 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 Problem A 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 Loop What is the net force on the current loop? What is the net torque on the loop?
Torque on the Current Loop At what angle is the torque a maximum value? At what angle is the torque a minimum value?
Sample Problem A 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?
Circular Motion in B-Field Right Hand Rule for Force Fingers point in direction of magnetic field B. Thumb points in direction of the velocity vector v. Palm shows the direction of the force F.
Mass Spectrometer F = qvB sin θ θ = 90 deg F = qvB F = ma a = v 2 /r F = mv 2 /r qvB = mv 2 /r m = qBr/v
Sample Problem A singly charged positive ion moving at 4.6 x 10 5 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 Spectrometer In 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 Problem The 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-Field Electrons are deflected downward. What is the direction of the magnetic field B?
Magnetic Flux Magnetic flux is the product of the average magnetic field times the perpendicular area that it penetrates.magnetic field
Magnetic Flux Illustrations The 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).magnetic fluxGauss' law for magnetism
Gauss’s Law for Magnetism The 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.magnetic flux
Sample Problem A 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?