You might wish to testimonial the Error Analysis part of the Prelab because that Physics 2212 laboratory #8, Capacitance and also RC Circuits.

You are watching: What does the slope of a force vs current graph represent The magnetic force, F, top top a current-carrying wire

F = IL×BorF = ILB sinθ

depends top top the existing through the wire, I, the size of cable in the magnetic field,L, the size of the magnetic field, B, and, because L andB are vectors, the angle θ in between the length of wire and also thefield. The accompanying illustration the this relationship is a view sketch—note the L and also B define a plane, and F must beperpendicular to the plane. The direction of (conventional) current defines the direction ofpositive L. This relationship will be examined two ways. First, a continuous current will be selected, andwires of various lengths will be placed perpendicular to a magnetic ar (θ=90°).The pressure magnitude will be measured. A graph the the force as a role of size should productivity a straightline of steep IB. Due to the fact that I is known, the size of the magnetic ar can be calculated.

Next, a specific wire length will it is in selected and placed perpendicular to a magnetic ar (θ=90°). Assorted currents will be passed with the wire, and also theresulting force magnitude will certainly be measured. A graph of the pressure as a role of existing shouldyield a directly line of slope LB. Since L is known, the magnitude of the magneticfield deserve to be calculated.

These two procedures of the magnetic field magnitude deserve to be contrasted to every other.

### Measuring the Force

Experimental Technique: one obvious method to execute this experiment is to placed a wire right into the field of a permanent magnet, passcurrent with the wire and measure the force on the wire. Then one deserve to vary the length, the currentand the angle to inspect out everything in the law. There room two difficulties with this. First its difficultto measure a force on a rigid cable (there will be current leads and other ingredient hanging on it whichconfuses matters). Secondly the leads associated to the sample cable might likewise experience part of themagnetic field and also this produces pressures which may confuse matters. The experiments we have actually designed foryou overcome both the these things easily.

Measuring the Force: Consider first figure above; the force is ~ above the cable which in this instance is up. Let united state assumethat the magnetic ar is created by a horseshoe magnet. Newton"s third Law tells us theremust be an same an opposite force downward ~ above the magnet. Instead of measure up theforce ~ above the wire, we might just also measure the pressure on the magnet. This is what wedo by place the magnet on the pan of a scale and measuring pressure as an noticeable weight.

An equal arm balance is depicted below. Originally the magnet is placed on the pan and a massM added to the other pan to restore equilibrium. Clear M would certainly be the massive of themagnet and the pressure of gravity on the magnet would be its weight, Mg. The cable is in thejaws the the magnet and also suspended rigidly native a stand which sit on the bench (it walk nottouch the magnet or scale). Now we send existing through the wire. There will certainly be a pressure F on the wire (let usassume up) and also therefore a force of reaction top top the magnet (down) bring about the magnet panto walk down, simply as though extr mass had actually been put on the pan. We currently addadditional fixed m come the massive pan and restore equilibrium. The gravitational forceon the additional mass m is mg, and also that exactly equates to the pressure on the magnetwhich subsequently is exactly equal come the pressure on the wire. Thus

F = mg = ILB sinθ

and we have our measure of the pressure on the wire.

(Of food if the direction of the present in the cable were reversed then the pressure onthe wire would be down, the force on the magnet up, and also to reclaim equilibrium a massm would have to be subtracted from the mass range pan. That is an equallygood way of doing things.)

The balance we usage in the laboratory is not actually an equal arm balance wheremasses should be included or subtracted. Quite it is a change arm type of balance wherein amass driver is relocated along the massive arm until the talk on the massive arm(clockwise) balances the talk on the range arm (counterclockwise). The variable arm has acalibrated scale significant on that so that the position of the rider tells you the actualmass on the scale pan. Wire Samples: These room made of a wide strip of steel deposited in the form of a rectangularU on an insulating plank (in fact a published Circuit or computer board). This isplaced in the magnetic field, as shown, so the the connecting central leg that theU is entirely in the field. That is ~ above this piece of the wire that us wish tomeasure force and also the pressure will be one of two people up or under (depending top top the currentdirection).

What about forces on the legs to the left and also right which action asleads to convey the existing to the wire? this legs will be partly in the magneticfield and experience some force. Make certain you have the right to think of at the very least one factor whythey do not matter.

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The wires are wide (about 2 mm). Think around whether you have to measure the outerlength (to outside the legs), the inner length (to within of the legs), or miscellaneous else.