Lecture 11Magnetic field

Generators and Transformers Motors

Galvanometers

Mass Spectrometer

Cyclotron.

3.7.1 The Magnetic Field

Permanent bar magnets have opposite poles on each end, called north and south. Like poles repel; opposites attract.

If a magnet is broken in half, each half has two poles:

By definition, magnetic field lines exit from the north pole of a magnet and enter at the south pole.

Magnetic field lines cannot cross, just as electric field lines cannot.

The Earth’s magnetic field resembles that of a bar magnet. However, since the north poles of compass needles point towards the north, the magnetic pole there is actually a south pole.

3.7.2 The Magnetic Force on Moving Charges

This is an experimental result – we observe it to be true. It is not a consequence of anything we’ve learned so far.

The magnetic force on a moving charge is actually used to define the magnetic field:

In order to figure out which direction the force is on a moving charge, you can use a right-hand rule. This gives the direction of the force on a positive charge; the force on a negative charge would be in the opposite direction.

Electricity and Magnetism

Electric forces hold atoms and molecules together. Electricity controls our thinking, feeling, muscles and metabolic processes. Electricity and magnetism underpin much of our current technology (e.g. computers). Electricity and magnetism are linked on a fundamental level.

Example 9:

An electron in a television picture tube moves toward the front of the tube with a speed

of along the x axis. Surrounding the neck of the tube are coils of wire that create a magnetic field of magnitude 0.025 T, directed at an angle of 60° to the x axis and lying in the xy plane. Calculate the magnetic force on the electron?

68.0 10 /m s

3.8 Generators and MotorsAn electric generator converts mechanical energy into electric energy:

An outside source of energy is used to turn the coil, thereby generating electricity.

An electric motor is exactly the opposite of a generator – it uses the torque on a current loop to create mechanical energy.

Electric Motor

An electric motor, is a machine which converts electrical energy into mechanical (rotational or kinetic) energy.

A current is passed through a loop which is immersed in a magnetic field. A force exists on the top leg of the loop which pulls the loop out of the paper, while a force on the bottom leg of the loop pushes the loop into the paper. The net effect of these forces is

to rotate the loop.

3.9 Transformers

A transformer is used to change voltage in an alternating current from one value to another.

By applying Faraday’s law of induction to both coils, we find:

Here, p stands for the primary coil and s the secondary.

The power in both circuits must be the same; therefore, if the voltage is lower, the current must be higher.

Example 11:

A step-up transformer is designed to have an output voltage of 2 200 V (rms) when the primary is connected across a 110-V (rms) source.

(a) If the primary winding has 80 turns, how many turns are required on the secondary?

(b) If a load resistor across the secondary draws a current of 1.50 A, what is the current in the primary, assuming ideal conditions?

(c) What If? If the transformer actually has an efficiency of 95.0%, what is the current in the primary when the secondary current is 1.20 A?

3.10 Galvanometer

A galvanometer is a device used to find direction of current and its magnitude. It has small resistance and is connected in series.

It consists of a coil of wire mounted so that it is free to rotate on a pivot in a magnetic field provided by a permanent magnet.

Once the instrument is properly calibrated, it can be used in conjunction with other circuit elements to measure either currents or potential differences.

3.11 Mass Spectrometry

• A mass spectrometer separates ions according to their mass-to-charge ratio. In one version of this device, known as the Bainbridge mass spectrometer, a beam of ions first passes through a velocity selector and then enters a second uniform magnetic field B0 that has the same direction as the magnetic field in the selector (see this figure). Upon entering the second magnetic field, the ions move in a semicircle of radius r before striking a detector array at P.

• If the ions are positively charged, the beam deflects upward, as Figure shows. If the ions are negatively charged, the beam deflects downward

• In practice, one usually measures the masses of various isotopes of a given ion, with the ions all carrying the same charge q. In this way, the mass ratios can be determined even if q is unknown.

• A variation of this technique was used by J. J. Thomson (1856–1940) in 1897 to measure the ratio e/me for electrons.

THE END