[FORCES ON CHARGES AND CURRENT-CARRYING WIRES IN MAGNETIC FIELDS]

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STUDIO Unit 12

Physics 2054 – College Physics

Last time we looked at the magnetic field around a wire or group of wires. We continue with this topic by including the forces that magnetic fields exert on charges and on wires.

We will begin with a discussion about what happens when a wayward charge finds itself moving in a magnetic field.

Unit 12 - FORCES ON CHARGES MOVING IN MAGNETIC FIELDS

Objectives

to understand the force on a moving charge in a magnetic field to understand the magnitude and direction of the force on a current-carrying wire

in a magnetic field to understand how two current carrying wires interact.

The Electric Field is a “reasonable” field and hopefully you have found it fairly easy to understand. The Magnetic Field is not quite so reasonable because it is a bit more complicated. You need to have read the first four sections of chapter 21 in order to easily follow the following material.

A stationary charge does NOT experience a force on it when it is placed into a magnetic field. A force only develops when the charge is moving in a magnetic field. Consider the

following diagram of a wood-screw:

This is a diagram of a right-handed screw. This means that if a screwdriver is used to drive the screw into a piece of wood, it must be turned in a clockwise direction. We use this rule to determine the direction of the force on moving charge in a magnetic field. Consider the next diagram stolen from the internet.

The equation that gives the magnitude of the force on a moving positive charge with velocity in a magnetic field is given by

where is the angle between and . The direction of the force is obtained by thinking of and as rigidly attached to each other and by thinking that these two vectors are rigidly connected to the head of a right handed screw. By turning into , the screw would advance in the direction that the force would be in. Notice that the force is perpendicular to both the velocity of the charge and the magnetic field. The diagram shows the fingers curled from to and the thumb winding up pointing in the direction of the magnetic force. The right hand rule is one of the most useful guides for understanding magnetic effects.

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Solve/answer the following in groups and be prepared to discuss your results.

(1) As derived from the force law (above), what are the units of the magnetic field? In SI units, this combination is defined as 1 Tesla (T). (You might find it interesting to look into Tesla’s biography!)

(2) A particle with a charge of +8.4 µC and a speed of 40 m/s enters a uniform magnetic field whose magnitude is 0.33 T. For each of the three cases in the drawing, calculate the magnitude and direction of the magnetic force on the particle.

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MERGEFORMATINET

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1.0a. The force on a moving charge in a magnetic field is always perpendicular to the velocity. Where else have you seen a force that behaves this way and what kind of motion resulted? (This is an important question so please don’t read ahead until you have answered it.)

For the type of motion that you described above, what are the critical parameters and what did you need to calculate them. Again, please do not look ahead until you have answered this question.

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b. At this point you should realize (unless of course you didn’t follow the directions above) that the motion is circular. The force points towards the center of the circle. Assume in the following that the magnetic force in this case has a magnitude equal to Bqv. This is true for motion in a plane with B perpendicular to the plane. The angle is therefore 90º. Take the mass of the particle as m.

Derive an equation for the radius of this motion in the space below. You do this by setting the magnetic force equal to the mass multiplied by the centripetal acceleration.

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c. How much time does it take for the mass to go around the circle once? What is this time called?

d. What is the frequency associated with this motion? (Derive it from the last part, don’t peek.) What is the angular frequency ?

e. Suppose the mass starts with an initial velocity that has a component parallel to the magnetic field. Describe the motion as best you can and draw a diagram. Again, try not to peek!

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MAGNETIC FORCES ON CURRENT CARRYING CONDUCTOR (A WIRE)

f. The Magnetic Swing Set

Equipment: Pictured below.

Let’s continue our discussion of forces in magnetic fields. Consider the following objects and how they are connected to build a magnetic swing set. We will be passing a current through the wire. A partial set-up is shown to the right of the diagram.

The swing is shown connected to the support (underside) while the power from the power supply (in current mode) is connected to the top. The connections go through the support. With this setup we can run a current through the three sides of the swing and, if we did so as shown, nothing much of interest would happen. We can now change this with the addition of a “Variable Gap Magnet”, a diagram of which is shown below.

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The Variable Gap Lab

Magnet consists of two 3/4 inch diameter neodymium magnets on an iron base. Two flat pole pieces are supplied to provide a uniform field when needed. The gap may be varied from 0.5 cm to 8.9 cm by turning the screws. The magnetic field strength (without the flat poles) varies approximately as shown in the Table. The magnet will not have a great effect on its surroundings because the field drops off to about 30 Gauss at the outside edges of the magnet. The older

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unit of magnetic field strength is the Gauss. 1 gauss=0.0001 T. We will use Teslas.

Gap (cm) Magnetic Field at Poles (Tesla/Gauss)

Magnetic Field at Midpoint between

Poles (Tesla/Gauss)0.5 0.75/7500 0.75/75001.0 0.60/6000 0.50/5000

8.9 0. 40/4000 0.007/70

The Variable Gap Magnet is shipped with the neodymium magnets installed. The neodymium magnets are attached only by magnetic attraction to the iron. If the magnets are removed for any reason, follow these instructions carefully to re-install them.

CAUTION: Be extremely careful when handling the neodymium magnets. The two magnets can snap together violently; any part of your body that is caught between the magnets may be severely injured.

The current in the wire swing can now interact with the magnetic field and we can see what happens. Having digested this material (above), we can proceed.

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g. Fill in the following information:

The size of the Gap metersEstimated B field based upon the data above. TeslaIdentify the N and S poles of the magnet.

When doing the last step, remember that if you use a compass, the strong field might just magnetize the compass the wrong way so keep its distance from the strong regions of the magnet.

For the following, refer to the following diagram:

Consider the current going in the direction shown to represent the movement (as usual) of positive charge. Based on this and the earlier material, what should happen to the current carrying wire if it were free to move? Explain this carefully. Remember that current is defined as the movement of positive charge and assume (reasonable) that the moving charges will drag the physical wire along with it (since it can’t leave it behind!).

What would happen if the direction of the current were reversed?

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h. Using the apparatus described above, perform the experiment and state whether your predictions were correct or not. If not, think it through again.

i. Measure the deflection (use one of the pole pieces as a reference) of the current element as a function of the current. At zero current the deflection is the equilibrium position.

current deflection0

j. How does the deflection vary with the current?

k. Change the magnetic field in the gap by changing the gap size. Using the calibration table, how does the new magnetic field compare with the old one? Repeat the current deflection experiment with the new magnetic field strength.

New Magnetic Field (T): _______________________T.

current deflection

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Compare these results with the previous results and state your conclusions.

1.1 a. In the last Unit you looked at the magnetic field of a current carrying conductor. If a current-carrying wire gives rise to a magnetic field, is it possible that a current in a wire can cause an interaction with another, parallel current-carrying wire? EXPLAIN.

b. Consider two wires with currents in the same direction.

(i) In the diagram below, draw the direction of the magnetic field due to wire 1 at wire 2, and the direction of the force on wire 2 due to wire 1. You do this by determining the direction of the magnetic field at wire 2 due to the current in wire 1. The direction of the force can be determined from what you learned above.

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Explain your results:

(ii) In the diagram below, draw the direction of the magnetic field due to wire 2 at wire 1, and the direction of the force on wire 1 due to wire 2.

Explain:

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c. Consider two wires with currents in the opposite direction.

(i) In the diagram below, draw the direction of the magnetic field due to wire 1 at wire 2, and the direction of the force on wire 2 due to wire 1.

(ii) In the diagram below, draw the direction of the magnetic field due to wire 2 at wire 1, and the direction of the force on wire 1 due to wire 2.

Explain:

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COMMENTS

The magnitude of the force on a current carrying conductor is given by

,

where I is the amount of current through the wire, l is the length of the wire, B is the magnitude of the magnetic field and is the angle between the magnetic field and the current. The magnetic field is measured in units of Tesla. The symbol for Tesla is T.

The direction of the force is given by a right hand rule.

SUMMARY

You should understand the magnitude and direction of the force on a current-carrying wire in a magnetic field. You should also be looking at the textbook!

EXERCISES: Complete these at home if there is no time remaining in the lab session.1) A magnet is placed near a current carrying wire as in the diagram below.

Determine the direction of the force on the wire.

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2) (from Arnold B. Arons, Homework and Test Question for Introductory Physics Teaching, John Wiley and Sons, Inc., NY, 1994.)

Two wires lie perpendicular to the plane of the paper and carry equal electric currents in the direction shown. Point P is equidistant from the two wires.

a) Construct a vector diagram showing the net magnetic field vector at point P. Explain your reasoning.

b) Suppose a third wire carrying equal current into the plane of the paper were located at P. What would be the direction of the force on this wire? Explain your reasoning.

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NOTES:

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