[FORCES ON CHARGES AND CURRENT-CARRYING WIRES IN MAGNETIC FIELDS]1 | P a g eSTUDIO Unit 12Physics 2054 – College PhysicsLast time we looked at the magneticfield around a wire or group ofwires. We continue with this topicby including the forces thatmagnetic fields exert on charges andon wires.We will begin with a discussionabout what happens when awayward charge finds itself movingin a magnetic field.Unit 12 - FORCES ON CHARGES MOVING IN MAGNETIC FIELDSObjectives- 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 wirein 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 tounderstand. The Magnetic Field is not quite so reasonable because it is a bit morecomplicated. You need to have read the first four sections of chapter 21 in order to easilyfollow the following material.A stationary charge does NOT experience a force on it when it is placed into a magneticfield. A force only develops when the charge is moving in a magnetic field. Consider thefollowing diagram of a wood-screw:This is a diagram of a right-handed screw. This means that if ascrewdriver is used to drive the screw into a piece of wood, itmust be turned in a clockwise direction. We use this rule todetermine the direction of the force on moving charge in amagnetic field. Consider the next diagram stolen from theinternet.The equation that gives the magnitude of the force on a movingpositive charge with velocity v in a magnetic field B is givenby)sin(vBqF where---  1800 is the angle between v and B. Thedirection of the force is obtained by thinking of v and B asrigidly attached to each other and by thinking that these twovectors are rigidly connected to the head of a right handedscrew. By turning v into B, the screw would advance in thedirection that the force would be in. Notice that the force isperpendicular to both the velocity of the charge and themagnetic field. The diagram shows the fingers curled from vto B and the thumb winding up pointing in the direction of themagnetic force. The right hand rule is one of the most useful guides for understandingmagnetic effects.2 | P a g eSolve/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 SIunits, this combination is defined as 1 Tesla (T). (You might find it interesting to lookinto Tesla’s biography!)(2) A particle with a charge of +8.4 µC and a speed of 40 m/s enters a uniform magneticfield whose magnitude is 0.33 T. For each of the three cases in the drawing, calculate themagnitude and direction of the magnetic force on the particle. INCLUDEPICTURE "http://www.webassign.net/CJ/21_02.gif" \*MERGEFORMATINET 3 | P a g e1.0a. The force on a moving charge in a magnetic field is always perpendicular to thevelocity. Where else have you seen a force that behaves this way and what kind ofmotion resulted? (This is an important question so please don’t read ahead until you haveanswered it.)For the type of motion that you described above, what are the critical parameters andwhat did you need to calculate them. Again, please do not look ahead until you haveanswered this question.4 | P a g eb. At this point you should realize (unless of course you didn’t follow the directionsabove) 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 toBqv. This is true for motion in a plane with B perpendicular to the plane. The angle - istherefore 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 settingthe magnetic force equal to the mass multiplied by the centripetal acceleration.5 | P a g ec. How much time does it take for the mass to go around the circle once? What is thistime called?d. What is the frequency associated with this motion? (Derive it from the last part, don’tpeek.) What is the angular frequency -?e. Suppose the mass starts with an initial velocity that has a component parallel to themagnetic field. Describe the motion as best you can and draw a diagram. Again, try notto peek!6 | P a g eMAGNETIC FORCES ON CURRENT CARRYING CONDUCTOR (A WIRE)f. The Magnetic Swing SetEquipment: Pictured below.Let’s continue our discussion of forces in magnetic fields. Consider the following objectsand how they are connected to build a magnetic swing set. We will be passing a currentthrough 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 powersupply (in current mode) is connected to the top. The connections go through thesupport. With this setup we can run a current through the three sides of the swing and, ifwe did so as shown, nothing much of interest would happen. We can now change thiswith the addition of a “Variable Gap Magnet”, a diagram of which is shown below.7 | P a g eThe Variable Gap Lab Magnet consists of two 3/4inch diameter neodymium magnets on an iron base.Two flat pole pieces are supplied to provide a uniformfield when needed. The gap may be varied from 0.5cm to 8.9 cm by turning the screws. The magneticfield strength (without the flat poles) variesapproximately as shown in theTable. The magnet will not havea great effect on itssurroundings because the fielddrops off to about 30 Gauss atthe outside edges of themagnet. The older unit ofmagnetic field strength is theGauss. 1 gauss=0.0001 T. Wewill use Teslas.Gap (cm) Magnetic Field at Poles(Tesla/Gauss)Magnetic Field atMidpoint betweenPoles (Tesla/Gauss)0.5 0.75/7500 0.75/75001.0 0.60/6000 0.50/50008.9 0. 40/4000 0.007/70The Variable Gap Magnet is shipped with the neodymium magnets installed. Theneodymium magnets are attached only by magnetic attraction to the iron. If the magnetsare removed for any reason, follow these instructions carefully to re-install them. CAUTION: Be extremely careful