Written by Dr. John K. Dayton MAGNETIC FIELDS THE MAGNETIC FIELD FORCES ON MOVING CHARGES THE MAGNETIC FIELD OF A LONG, STRAIGHT WIRE THE MAGNETIC FIELD OF A LOOP OR COIL THE MAGNETIC FIELD OF A SOLENOID

THE MAGNETIC FIELD: N S The magnetic field is designated by the symbol B. The source of all magnetic fields are moving electric charges. Even the magnetic fields associated with electromagnetic radiation have their source in moving electric charge. The SI unit for the magnetic field is the tesla, T. A more common unit of magnetic field strength is the gauss, G. Earth’s magnetic field at the surface is about 0.5 G G  1T The magnetic field is characterized by what we call a north and a south pole. Similar poles repel and opposite poles attract. Outside of magnetic materials magnetic field lines extend away from north poles and toward south poles. However, magnetic field lines, unlike electric field lines, are continuous. Each magnetic field line forms a complete loop. The simplest of all magnetic fields is the magnetic dipole, like a bar magnet.. Magnetic monopoles, such as an isolated north pole, do not exist.

EXAMPLE:A proton traveling horizontally to the right with a speed of 1.5 x 10 4 m/s encounters a uniform magnetic field of 0.55T oriented 60 o above the horizontal. What is the magnitude of the force on the proton and what is its initial direction? B v +e According to the right-hand-rule this force will be directed outward from the diagram.

According to the vectors shown in the diagram, and the right-hand-rule, q must be a negative charge. Using the right-hand-rule, can you determine the sign of q in the diagram? Click for the answer.

B q Is the charge q of the moving particle positive or negative? q is positive. B out of diagram view from above v FBFB v

EXAMPLE: An alpha particle, q = 6.4 x C and m = 6.68 x kg, is following a circular path of radius 0.5m in a uniform magnetic field of 1.2 T. (a) What is the angular speed of the alpha particle? (b) What is the linear speed of the alpha particle?

EXAMPLE: Calculate the net force on a wire of length 20m and carrying a current of 12A through a magnetic field of 0.5 Gauss directed 70 o to the wire. B 12A 20m According to the right-hand-rule, this force will be directed outward from the diagram.

EXAMPLE:A coil of wire composed of 100 turns of radius 6cm carries a current of 5A. It is in a uniform magnetic field 0f 0.65T oriented 75 o to the plane of the coil. (a) What is the magnetic moment of the coil? (b) What is the torque on the coil?  is the angle between B and m.  = 90 o – 75 o

Calculate the magnetic field mid way between the two wires.

EXAMPLE:The central conducting wire of a coaxial cable carries a current of 3A upward. The outer, cylindrical conducting wire of radius 3mm carries a uniformly distributed current of 5A downward. What are the magnetic field strengths at 2mm from the center and 5cm from the center of this wire? Only the net enclosed current is used. I enc =5A- 3A. The net current for B 1 is upward and the net current for B 2 is downward so these two fields are oriented in opposite directions.

EXAMPLE:A long straight, vertical wire carries a current of 5A upward. Near the wire is a rectangular loop of wire carrying a current of 3A. The loop has dimensions 5cm by 10cm and is positioned so that its long side is parallel to the long wire at a distance of 5cm with its current also directed upward. What is the net force on the loop? I 1 =5A I 2 =3A 5cm 10cm wire loop F2F2 F4F4 The magnetic field produced by the wire in the plane of the loop is directed inward, into the diagram. The strength of this field decreases as you move further from the wire. The force on side 1 is downward and the force on side 3 is upward. Use the right- hand-rule to confirm this. These forces are of equal magnitudes so cancel each other out. The force on side 2 is toward the wire and the force on side 4 is away from the wire. These are also in opposite directions but the force on side 2 is stronger because it is closer to the wire. B from the wire is inward on this side of the wire Solution continues on next slide.

continued from previous slide F net is directed toward the wire.

EXAMPLE:Calculate the magnetic field strength at the center of a coil of radius 20cm, 200 turn of wire, and carrying a current of 2.5A.

EXAMPLE: A solenoid is to be made so that a magnetic field of 0.5T is at its center. If the solenoid is to be 10cm in length and wrapped with wire carrying a current of 3A, how many turns of wire are required?