Figure 638 shows the resultant magnetic field in this case. If the current was reversed, then the wire would be catapulted inwards.
movement
magnetic field
current
Figure 638 The motor effect
The direction of the force experienced by moving currents in a magnetic field can be determined by the vector addition of the two fields. However, an easier way for determining the direction of the force is to use a right-hand palm rule or Fleming’s left-hand rule. There are a variety of hand rules used and it very much depends on the textbook you use as to what rules will be given. It is really up to you to use the hand rule that you prefer. Figure 639 shows three “hand rules” commonly used.
F
I B
Thumb points in direction of current Fingers point
along lines of magnetic field
Force comes out of palm
Figure (a)
B
F I
Thumb points in direction of force
Current points along lines of magnetic field
Magnetic field comes out of palm
Figure (b)
B
I F
Field along first finger
Current along second finger
Force along thumb Left Hand
Figure (c)
Figure 639 Hand rules used to show the direction of force.
In Figure 639 (a), if the fingers of your right hand point in the direction of the magnetic field B, and your thumb points in the direction of the conventional current, then your palm points in the direction of the force. This rule is called the right-hand palm rule. An alternative to this
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ORE
is shown in Figure 639 (b). (This is the rule preferrd by the
author because the fingers give a sense of flow of conventional current and the palm points north-south like a bar magnet and the thumb is the direction of movement or force).
Figure 639 (c) is Fleming’s left hand rule. The first finger gives the direction of the magnetic field, the second finger gives the direction of conventional current, and the thumb gives the movement or force direction
Try these rules for the examples in Figures 637 and 638 to see which one you prefer.
Note that these rules are for conventional current and not true electron flow. If electron flow is to be determined, apply a rule of choice and find the force for conventional flow, say north – then state your answer as the opposite direction, in this case south.
6.3.4 FORCEONA
MOVINGCHARGE
As stated, stationary charges experience no force in a magnetic field. However, if charged particles move in a magnetic field, a force is exerted on them. This force causes them to deflect if they are not confined in a conductor.
The same hand rules can be used to determine the direction of the force experience on a charge. However, remember that they apply to moving positive charge. If an electron is moving, as is more commonly the case, remember to apply the rule and then reverse the force direction.
When the positive charges move as shown in Figure 640, they will experience an upwards force. Check this for yourself using one of the hand rules.
+ + + + + +
F
B
Direction of charge movement moving positive
charge, q
N
S
Figure 640 Force on a moving charge
6.3.5 MAGNITUDE
OFMOVING
CURRENTSANDCHARGES
When an electric current flows in a conductor, and the conductor is placed in a magnetic field, the force on the conductor is due to the individual forces on each of the individual charges in the conductor. The magnitude of the magnetic force F is found to be directly proportional to:
1. the strength of the magnetic field B measured in teslas (T)
2. the current flowing in the wire I measured in amperes (A)
3. the length of the conductor in the magnetic field l measured in metres (m).
So that
F = IlB
This force is greatest when the magnetic field is perpendicular to the conductor. Sometimes the wire in the magnetic field is at an angle θ to the magnetic field. In this case
F = IlB sin θ
Therefore, as θ decreases, so too does the force. When
θ = 0° the current in the conductor is moving parallel to
the magnetic field and no force on the conductor occurs.
The force experienced can be increased if the number of turns of wire carrying the current is increased. In this case the force is given by F = Il B n where n is the number of turns of wire. When there are a number of turns of wire suspended between a magnetic field, the device is commonly called a wire toroid.
In order to determine the magnitude of the force experienced by a single point charge q, we will follow through the following derivation.
The velocity of the particle is given by
v displacement time --- s t -- = =
If the length of the charge carrier is l, then
v l t
-⇔l v t
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But, q = It ⇔ Ι = q / t and F = I lB
By substitution, the force on an individual charge is given by
F q t ---×( )vt ×B = That is, F = qvB
If a charged particle enters a uniform magnetic field at an angle other than 90°, the force it experiences is given by
F = qvB sinθ
When θ = 90°, and the magnetic field is uniform, the particle will undergo uniform circular motion as the force it experiences is at right angles to its motion. The radius of its circular motion is given by:
qvB mv 2 r ---⇔r mv qB --- = =
When the particle enters the field at an angle other than a right angle, it will follow a helical path.