Electromagnetic fields

(A) Concept of electromagnetic field

Field around a current carrying conductor

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The force is given by the equation

   F= BiL sinO

Where F = force, i= current in the conductor, B= Electromagnetic field, L= length.

Note: the greatest force occurs when O=90° i.e when the conductor is at the right angle to the field. The units of B is Tesla or Weber per square metre (Wbm^-2)

One Tesla is defined as force per unit length on a wire carrying a current of one ampere at right angle to the field.

The magnetic flux (¢) passing through a surface is BA, where A is the area of the surface at right angles to the field, ¢= BA,

Magnetic flux (¢) is measured in Weber’s (Wb).  ¢ = BAcosO

The force on a moving charge in a magnetic field is expressed as F= qvBsin

Force and field patterns of two current carrying conductors can be expressed as 

F/l = u₀ i₁ i₂ / 2πr

U₀ = permeability of vacuum = 4π × 10^-7 Am^-1 and r is the separation.

Current flowing in two long parallel wires

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Moving coil galvanometer

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D.c motor

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(B)Electromagnetic flux induction

Faraday’s experiment

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Faraday’s law of e-m induction

Whenever there is a change in the magnetic flux linked with a circuit, an Electromotive force, E is induced, the strength of which is proportional to the rate of change of the flux ¢ linked with the circuit. The faster the flux is changed the greater is the e.m.f produced. E= – d¢/ dt

Lenz’s law of e-m induction

The direction of the induced e.m.f. is such that it tends to oppose the change that produced it.

Fleming’s right-hand rule

If the thumb and the first two fingers of the right hand are held at right angles to each other and the first finger is pointed in the direction of the magnetic field and the thumb in the direction of motion, the second finger gives the direction of the induced current.

A.c generator

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Note that the laws of Electromagnetic induction [when the magnetic flux through a coil changes, the e.m.f, E generated in the coil] can be expressed as E= Nd¢/dt

Where N is the number of turns in the coil, N¢ is the flux linkage and d(N¢)/dt is the rate of change of flux linkage in Weber’s per second (Wbs^-1).

E.M.F generated in a rotating coil of N turns and area A being rotated at a constant angular velocity w in a magnetic field of flux density B with its axis perpendicular to the field. E= B ANwsint

(C) Inductance

The e.m.f generated is given as E= LdI/ dt

The unit of inductance is the Henry (H) and it is defined as the inductance of a coil (or circuit) in which an e.m.f of one volt is induced when the current changes at the rate of one ampere per second.

 The energy stored in an inductor; the energy, W, stored in an inductor of inductance, L is W= ½ Li² the energy is used to produce the magnetic field in and around the coil.

(D)Eddy currents

Eddy current can be used as Electromagnetic damping, to melt metals in a vacuum so making metals of a high purity free from atmospheric contamination and to heat metal parts of valves.

Speedometer

A rotating magnet driven by a flexible cable sets up Eddy currents in a pivoted aluminum disc. The magnetic reaction of the Eddy currents sets up a couple on the disc which varies with the speed of the car.

(E)Transformer

A simple transformer

Source: www.commons.wikimedia.org 

V_s and V_p are known as the induced e.m.f of the secondary and primary coil respectively. Where N_s and N_p are the number of turns on the secondary and primary coil and I_p and I_s are the currents flowing in the primary and secondary coil.

    This is the ideal transformer and this equation hold  V_s / V_p = N_s / N_p = I_p / I_s

The transmission of electricity

Electrical energy is generated in power stations by generators at a potential of about 25kV. It is first stepped up to 400kV by a transformer and then transmitted across the country in aluminum cables roughly 2cm in diameter.

Induction coil

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Past questions

1.A house is supplied with a 240V a.c mains. To operate a doorbell rated at 8V, a transformer is used. If the number of turns in the primary coil of the transformer is 900, calculate the number of turns in the secondary coil of the transformer. (Wassce 1991)

A. 30

B. 240

C. 248

D. 450

E. 1248

Answer: A

Solution: E_p / E_s = n_p / n_s = 240/900 = 8/n_s;

n_s = 8×900/ 240 = 30

2. An induction coil is generally used to? (Wassce 1991)

A. Rectify an alternating current

B. Produce a large input voltage

C. Smoothen a pushing direct

D. Modulate an incoming radio signal

E. Produce a large output voltage 

Answer: E

3. The material used for constructing the core of an Electromagnet is? (Wassce 2001)

A. Iron

B. Carbon

C. Copper

D. Steel

Answer: A

4. A transformer has 400turns of wire in the primary coil and 40turns in the secondary coil. If the input voltage is 150volts, calculate the magnitude of the output voltage. (Wassce 2014)

A. 150V

B. 55V

C. 36V

D. 15V

Answer: D

Solution: N_p= 400, N_s= 40, E_p= 150, E_s= ?

From the formula: E_s / E_p= N_s / N_p 

E_s = E_pN_s / N_p = 150×40 400 =15V

5. A transformer has a primary coil with 500 turns and a secondary coil with 2500turns. When the voltage input to the primary coil is 120V, the output is? (Jamb 1985)

A. 6000V

B. 600V

C. 240V

D. 60V

E. 24V

Answer: B

Solution: V_p / V_s = N_p / N_s = I_s / l_p

500/2500 = 120/V_s ;.    V_s = 600volts 

6. The d.c generator has essentially the same components as the a.c generator except the presence of? (Jamb 2008)

A. Slip-ring 

B. Carbon brushes

C. Split ring 

D. Armature

Answer: C

7. Power supply is transmitted at a very high voltage and low current in order to? (Jamb 2010)

A. Increase the power supply

B. Prevent overheating of the coil

C. Make it travel fast

D. Make it pass through the transformers.

Answer: B

8. Induced emfs are best explained using? (Jamb 2013)

A. Ohm’s law

B. Faraday’s law

C. Coulomb’s law

D. Lenz’s law

Answer: D