3. Electromagnets and Forces
Magnetic Fields around Wires
A conductor carrying an electric current is always surrounded by a magnetic field.
That’s right: every current-carrying wire becomes a magnet!
Electromagnetism is a temporary effect caused by the flow of electric current and it disappears when the current flow is stopped.
The magnetic field lines due to the current in a straight wire are concentric circles with the wire at the centre. The direction of the magnetic field can be found using the right-hand screw (grip) rule.
The wire is gripped with the right hand so that the thumb lines up with the direction of current flow. The direction of the magnetic field is given by the curl of the fingers.
The strength of the magnetic field caused by the flow of current is given by B = (k is a constant).
Drawing 3D Direction
Remember: the direction of the current is the direction of positively charged particles. When the electrons are moving in one direction the conventional current is in the opposite direction.
To represent three dimensional situations on a two dimensional page, use the following convention.
CurrentField lines
Current Field lines
Forces between two parallel wires
Below, two wires are viewed from above. They have current flowing in opposite directions.
In between the two wires above, we can see that the field direction is the same for both wires: down. As “likes repel”, this means that these two wires will repel each other.
Loops of wire are called solenoids
The electromagnetic effect of a current-carrying conductor can be magnified by using a conductor shaped into a loop or series of coils.
Thus, we can create a bar magnet using a solenoid with current flowing through it. This is called an electromagnet. The benefits of an electromagnet over a permanent bar magnet are that
- it can be turned on and off as required
- it’s field direction can be changed (ie. It’s poles can be reversed)
Alternative method to find direction: the Solenoid Rule
Grip the entire coil with the right hand with the fingers wrapped in the direction of the current flow, and the thumb will point to the North pole or in the direction of the magnetic field inside the coil. This is often called the right hand solenoid rule. Test the two methods on the loops of wire below.
The force on a current carrying wire in a magnetic field
Remember that
- For a current-carrying conductor there is an associated magnetic field
(The direction of the field is given by the right-hand grip rule)
A consequence of this is that
- For a current-carrying conductor in a magnetic field there is a force acting on it.
(The direction of the force can be determined by the right hand slap rule.)
In this rule, the hand is opened flat and the fingers are aligned with the magnetic field. The thumb is pointed in the direction of current flow and the palm is now facing the direction of the force.
Why is there a force on the wire?
The two magnetic fields will interact (as with two north poles repelling each other) and a force will be produced. So if we have two wires parallel to each other, each carrying a current, then both will be simultaneously creating its own magnetic field and under the influence of the other’s magnetic field.
How strong is the force?
If the field is perpendicular to the flow of current, the force on a current-carrying wire in a magnetic field is proportional to the current, the length of wire in the field, and the strength of the field.
B
Note: When = 900, sin = 1 F = nBIL When = 00, then sin = 0, F= BiLsin = 0 .
Applet: Lorentz Force
The force on a moving charge
The force is on the wire is due to forces on the individual electrons moving in the wire.
When the electrons are constrained to move within a conductor, then the force becomes the force acting on the wire.
A moving charge can be considered to be an electric current.
Consequently, a charge moving through a magnetic field will experience a force in the same way as a current carrying conductor would.
The experiment on the left shows a cathode ray being bent by a magnetic field towards the top.
If the force on a charge remains perpendicular to its motion, the charge will move in a circular arc. (This is the same as an object attached to a string being swung in a horizontal plane – the motion will be circular.)
Generally, the magnitude of these forces is very small (in the order of 10-11N)
but they are not insignificant because the mass of an electron is 9.1 10-31 kg,
so deflections can be quite large
Examples for class discussion
Figure 4 below shows a single loop of wire in a uniform magnetic field. The loop can rotate, and is shown at three different orientations. In each case there is a current flowing around the coil from W to X to Y to Z.
1998 Question 6
The magnetic field is 0.10 T, and the current in the loop is 0.30 A. With the loop in orientation (a) of Figure 4, what is the magnitude of the force acting on side WX of the coil? The length of side WX is 0.030 m. Show yourworking.
1998 Question 7
In Figure 5 below, the arrows indicate possible directions of the force on side WX of the loop in the three orientations (a), (b) and (c). The arrows in each orientation are in a plane perpendicular to the axis of rotationof the loop.
For each orientation in Figure 5, circle the head of the arrow which best represents the direction of themagnetic force on side WX of the coil. If there is no force on the side, write NF under the diagram.
In Figure 6 below, the arrows indicate possible directions of the force on side XY for the loop in orientations (a) and (c) shown in Figure 4.
1998 Question 8
For each of the two orientations in Figure 6, circle the head of the arrow which best represents the direction of the magnetic force on side XY of the coil. If there is no force on the side, write NF under the diagram.
Class discussion suggested points
1998 Question 6
F = nBIL
F = 1 × 0.010 × 0.30 × 0.30
F = 0.0009 N
= 9 × 10-4 N
1998 Question 7
a) pointing to the leftb) pointing to the leftc) pointing to the left
(a)The field is down, the current is into the page, so the thumb points into the page with the fingers pointing down. This makes the palm of your hand face left, so the force is in the direction pointing to the left
(b)The field is down, the current is into the page, so the thumb points into the page with the fingers pointing down. This makes the palm of your hand face left, so the force is in the direction pointing to the left
(c)The field is down, the current is into the page, so the thumb points into the page with the fingers pointing down. This makes the palm of your hand face left, so the force is in the direction pointing to the left
There isn't any change in the 3 orientations, the field was constant, and the wire had a current going into the page in these three situations, so each answer has to be identical. Don't get fussed that on the exam, they actually gave you such a simple question. You need to solve every problem on its merits.
1998 Question 8
a) NFb) Into the plane of the page
(a)The section of wire XY is parallel to the field, so this means that the force acting on it will be zero.
(b)Now the wire is at right angles to the field, so there will be a force acting on it. The field is down the page (direction of your fingers) the current is from left to right across the page (direction of your thumb). So your palm must be facing into the page (you need a flexible wrist for this). So the force is into the plane of the page. Remember that you need to circle the head of the arrow.