Lorentz Force Law F= I L ´ B

We discussed in the lab on drawing electric field lines, how force is related to electric field. If a particle has a charge q₀ and is in an electric field E, then it experiences a force F which is proportional to both the charge and the electric field and is in the same direction as the electric field.

The case of a magnetic field is a bit more complicated. For a particle in a magnetic field to experience a force, the particle must have a charge and must be moving (i.e. have a velocity). If the velocity v and the magnetic field B are in the same direction (parallel), there is no force. More generally, the magnitude of the force is proportional to the magnitude of the velocity, the magnitude of the magnetic field and the sine of the angle between them. The direction of the force is perpendicular to the plane in which the other two vectors (v and B) lie. Putting it all together yields

If you have a bunch of charged particles moving, it is known as a current. In such a case, the equation above can be rewritten as

where I is the current and L is the length of the wire. Verify that q₀v and IL have the same dimensions.

Part I

• Attach the current arm (see figure below) to a ringstand.
  

• Insert a current loop (see figure below) into the end of the current arm. You will find holes on the ends of the current arm. (Use only the ones labeled SF 37-40.)
  

• Record the horizontal length of the loop. Why only the horizontal?
• Place the magnet on the pan balance and find its mass to the nearest tenth of a gram. The effects we are looking for are small, try to measure the mass carefully.

  Mass of magnet

• Set up the current arm such that the bottom part of the current loop in passing through the magnet (which is still on the pan balance). Make sure it is not touching the magnet. (See figure below.)
  

• Connect the current arm (you will find holes on top of it) and an ammeter (in series, of course) to a power supply. (See figure below.) Make sure the power supply is on DC. If you find your power supply isn't working, try pressing the (circuit breaker) button in the back.
  

Ammeters measure current. You will see several settings on your ammeter. One setting tells the meter to expect DC currents. Another setting tells the meter the maximum current you expect to be reading. Set it at 10 A. A needle points to a number between 0 and 100 telling you what percentage of your maximum current is going through the ammeter. Notice the mirror behind the needle. It tells you when you are looking straight on - when you see just one needle, not the needle at its reflection. Turn your power supply off and make sure the needle on your ammeter is at zero. That little screw head is what you use to adjust the needle. The ammeters were meant to lie flat, not sit up on their edge.

Measurements I

• Send a current of 1 amp through the circuit.
• The pan balance should no longer be balanced. Why? (Hint: it involvesF= I L ´ B and Newton's Third Law.)
• Adjust the balance and find the magnitude of the additional force.
• Repeat for I=2,3,4 and 5 amps.
• Plot F versus I. Fit to a straight line. What is the slope? (Not the number but what is it physically.)
• Extract B. What are its units?

Measurements II

• Reverse the leads in the the current arm and repeat the above measurements and plotting. Reversing the current should this change the direction of the current.
  Length =

  Current	Change in mass      (sign included)	Force

• Make a note of which way the current is flowing through the horizontal part of the circuit element. Also note the orientation of the magnet (which color is on which side). Make a drawing. This drawing must appear in your report.
• For this drawing determine the direction of the Lorentz force.
• Determine the direction of the magnetic field using the right-hand rule.

Measurements III

• Replace the current loop used above and find the additional force for I=2 amp.
• Repeat for a total of four lengths (SF 37, 38, 39 and 40).
• Plot F versus L. Fit to a straight line. What is the slope? Physically, not just a number.
• Extract B. How does it compare to the result above?