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**Welcome to class! **

In today’s class, we will be talking more about the magnetic field. Enjoy the class!

**Magnetic Field II**

**The magnetic field of a current-carrying conductor**

A wire (conductor) carrying an electric current has a magnetic field around it, i.e. it behaves like a magnet. See diagram below.

A compass needle is deflected when placed near a current-carrying conductor. The sense of the deflection is reversed if the current direction is reversed. For a straight conductor, the direction of the magnetic field is given by Maxwell’s right-hand screw rule or the clenched fist rule.

**Maxwell’s right-hand screw rule**

If a right-handed screw is turned such that its point travels along the direction of the current, the direction of rotation of the screw is the direction of the magnetic field.

**Clenched fist rule**

If the wire is grasped with the right hand such that the thumb points in the direction of the current, the direction of the curled fingers is the direction of the magnetic field.

**Circular conductor**

For a circular coil carrying a current, the face of the coil at which the current is seen to flow clockwise is an S-pole while the other face is the N-pole of the magnetic field.

**Solenoid**

For a solenoid (i.e. along with the cylindrical coil of insulated wire) carrying a current, the direction of the field is determined using any of the above rules.

**Force on a current-carrying conductor**

A current-carrying conductor placed in a magnetic field experience a force.

The force is directly proportional to:

- The magnetic field strength
- The current in the conductor, and
- The length of the conductor

The force is largest when the direction of current is perpendicular to the magnetic field, and it is zero when the current flows in the direction of the magnetic field. The direction of the force can be determined using *Fleming’s left-hand rule:*

*It states that if the thumb, forefinger and the middle finger of the left hand are held mutually at right angles with the forefinger pointing in the direction of the magnetic field and the middle finger in the direction of the current, the thumb will point in the direction of the force. *

Using this rule, the direction of the force on the conductor figure (a) is into the paper, while that of figure (b) is out of the paper.

**Two parallel current-carrying conductors**

A magnetic field is set up around each of two parallel conductors which carry electric currents. The interaction of the fields results in a mutual force of attraction or repulsion between the conductors. The magnetic of the field is:

- directly proportional to the product of the currents in the conductors and the length of conductors, and
- inversely proportional to the distance between them.

The force is attractive if the two currents are in the same direction, but repulsive when flowing in opposite directions. See diagram below.

**Charged particle moving in a magnetic field**

The current flowing in a conductor is the sum total of the motions of the individual charges. Therefore the force on a current-carrying conductor is the sum total of the forces on individual charges. The force F on a charge q moving with velocity v in a magnetic field of strength B is given by the formula:

F = qvB sin

Where is the angle between v and B. when v and B are in the same direction, the angle is equal to zero and from the equation above the force is equals to zero because sin = sin0° = 0. When V and B are at right angles, then sin = sin 90° = 1 and F is given by

F = qvB

**Worked example**

(1) Find the magnetic force experienced by an electron projected into a magnetic field of flux density 10 Tesla with a velocity of 5 x 10^{7}m/s and in a direction

(i) 90°

(ii) 60°

(iii) parallel to the magnetic field. Assume charge on an electron = 1.6 x10^{-19}C

If the wire is grasped with the right hand such that the thumb points in the direction of the current, the direction of the curled fingers is the direction of the magnetic field.

**Circular conductor**

For a circular coil carrying a current, the face of the coil at which the current is seen to flow clockwise is an S-pole while the other face is the N-pole of the magnetic field.

**Solenoid**

For a solenoid (i.e. along with the cylindrical coil of insulated wire) carrying a current, the direction of the field is determined using any of the above rules.

**Applications of an electromagnetic field**

Electromagnetic field finds many common applications in industry:

- They are used in the construction of such electromagnetic devices as the Electric bell and the telephone earpiece
- They can be used to separate iron from mixtures containing non-magnetic substances.
- In producing intense magnetic fields such as those required in generators and electric motors.

**General evaluation**

**(1)** Find the magnetic force experienced by an electron of charge 1.6 x 10-19C projected into a magnetic field of flux density 10T, with a velocity of 3 x 107m/s, in a direction.

(i) Parallel to the field

(ii) at a right angle to the field

(iii) at 30° to the field.

**Assignment**

**(1)** Write down the expression for the force exerted by a magnetic field on a moving charge. Define the terms used in the expression and also use it to calculate the force on an aeroplane which has acquired a net charge of 100C and moves with a velocity of 300 m/s perpendicular to the Earth’s magnetic field of 5 x10^{-5}T.

In our next class, we will be talking about** Electromagnetic Field.** We hope you enjoyed the class.

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