Magnetism and Currents

A current generates a magnetic field. A magnetic field exerts a force on a current. Two contiguous conductors, carrying currents, will exert forces on each other. In this section we learn that:

Magnetic Force on Current-Carrying Wire We saw that magnetic fields, exert forces on moving charges. But moving charges constitute a current (either in vacuum or inside a conductor) Thus, a current-carrying wire will experience a force when placed in a magnetic field

Magnetic Force on Current-Carrying Wire If a segment of a wire of length L carries a current I, in a region of space where there is a magnetic field B, then the wire experiences a force F given by: The force is perpendicular to the current according to the right hand rule: point fingers in the direction of the current, rotate or close towards magnetic filed,  thumb points in the direction of the force

Magnetic Force on Current-Carrying Wire A cooper rod 0.15 m in length, and 0.05 kg in mass, is suspended from two thin, flexible wires, in a magnetic field B = T, as shown. Find: a)The direction b)The magnitude of the current I needed to levitate the rod

Magnetic Forces on a Current Loop A rectangular current loop in a magnetic field The force on each horizontal segment is zero (I  B). The force on each vertical segment is F = I L B The two forces are equal and opposite  The loop is not displaced However the forces exert a torque on the loop  The loop will rotate

Magnetic Forces on a Current Loop The torque exerted by the magnetic force on the loop is: In general, for an arbitrary field-loop orientation: For a loop with N turns and area A

Torque on a Coil A rectangular coil with 200 turns, is placed in a magnetic field B = 0.35 T. If the maximum torque is 0.22 N m, what is the current I on the coil?

Magnetic Field Produced by a Current It was experimentally found that currents produce magnetic fields For a straight long wire, that carries a current I, the lines of the magnetic field B created by the current, are circles, centered at the wire, and perpendicular to it. The direction of the magnetic field is given by the right hand rule, as shown above.

Magnetic Field Produced by a Current Ampere’s Law is used to calculate the magnetic field produced by a current (or current-carrying wire) Calculated along a closed path  0 = 4  x10 -7 T m / A = permeability of free space B || is the magnetic field parallel to the path

Magnetic Field Produced by a Current Ampere’s Law For an infinite straight wire with current I 1.Path is circular loop with radius r centered at wire and perpendicular to it 2.Segments are  L all around the loop 3.B lines are circles around the loop (empirical) so B || = B all around, and  B ||  L = B 2  r 4.I enclosed = I  B 2  r =  0 I 1.Define the closed path 2.Divide the path in segments 3.Calculate  B ||  L 4.Equate to  0 I enclosed

Magnetic Field Produced by a Current For a long straight wire, that carries a current I, the lines of the magnetic field B created by the current, are circles, centered at the wire, and perpendicular to it. The direction of the magnetic field is given by the right hand rule, as shown below. The magnitude of the magnetic field is:

The wire carries a current of 2.4 Amp. The particle has a charge of 52  C, moves with a speed of 720 m/s and is at a distance of 13 cm from the wire. Find the force on the particle

Force between two current-carrying wires I1I1 I2I2 d We know that a current I produces a magnetic field B, at a distance r, given by: We know that a current I, in a magnetic field B, experiences a force F, given by: Calculate the force exerted on each other, by two parallel conductors (length L, current I), separated by a distance d. Is the force attractive or repulsive? What happens if one current is reversed?

Magnetic Field of a Current Loop I At the center of the loop: For a loop with N turns: Note that the magnetic field of a loop is similar to the magnetic field of a magnet bar

If the currents are in the same direction the two loops attract each other If the currents are in opposite directions the two loops repel Magnetic Forces Between Current Loops

Magnetic Field of a Solenoid A solenoid is a long wire wound into a succession of closely spaced loops The magnetic field inside the solenoid is: Ideally, for a very long solenoid, the magnetic field is zero outside the solenoid, and parallel to the axis, and uniform in strength, inside.

Magnetic Field of a Solenoid What would happen if we place a magnet bar near the solenoid?

A Solenoid.. is a closely wound coil having n turns per unit length. current flows out of plane current flows into plane What direction is the magnetic field?

A Solenoid.. is a closely wound coil having n turns per unit length. current flows out of plane current flows into plane

A Solenoid Consider longer and longer solenoids. Fields get weaker and weaker outside.

Apply Ampere’s Law to the loop shown. Is there a net enclosed current? In what direction does the field point? What is the magnetic field inside the solenoid? current flows out of plane current flows into plane

Apply Ampere’s Law to the loop shown. Is there a net enclosed current? In what direction does the field point? What is the magnetic field inside the solenoid? current flows out of plane current flows into plane

Magnetic Materials The phenomenon of magnetism is due mainly to the orbital motion of electrons inside materials, as well as to the intrinsic magnetic moment of electrons (spin). There are three types of magnetic behavior in bulk matter: Ferromagnetism Paramagnetism Diamagnetism Remind me to ask you: why does the magnet stick to the refrigerator?