Magnetic Field

If a charged particle is projected in a magnetic field, in general, it experiences a magnetic force. By projecting the particle in different direction from the same point P with different speeds, we can observe the following facts about the magnetic field force.

a.       Force experienced by the moving charge is directly proportional to the magnitude of the charge i.e.

F α q

b.       Force experienced by the moving charge is directly proportional to the component of velocity perpendicular to the direction of magnetic field i.e.

F α v sinθ

c.       The magnitude of the force F is directly proportional to the magnitude of the magnetic field applied i.e.

F α B

On combining all factors we get,

F = kq v sinθ B

Here k=1 is proportionality constant. F= q v sinθ B. Here we can see that v and B follows the vector product hence force is perpendicular to v and B. Direction of the force can be can by Right Handed Screw Rule or Right Hand Rule.

  

By measuring the magnetic force F acting on a charge q moving at a speed v, we can obtain B. If v=1, q=1 and sinθ =1 or θ=90º then F = 1x 1x B x 1 =B

Thus the magnetic field induction at a point in the field is equal to the force experienced by a unit charge moving with a unit velocity perpendicular to the direction of magnetic field at that point.

Special Cases

a.       If θ =0º or 180º the F = q v Bsin(0) = 0. Its means, a charged particle moving parallel to the direction of magnetic field, does not experience any force.

b.      If θ =90º or 180º the F = q v Bsin(90) = qvB (maximum force). Its means, a charged particle moving along a perpendicular to the direction of magnetic field, it experiences maximum force.

c.       If v =0, then F=q v sinθ B = 0. It means, a charged particle is at rest in a magnetic field, it experiences maximum force. It experiences no force.

UNIT OF MAGNETIC FIELD B

SI unit of magnetic field is tesla (T) or Weber /meter²

1T = 1NA^-1m^-1

1 Gauss = 10^-4 T

Dimensions of B = [MA^-1T^-2]

We have a magnetic field of the order of 10^-5 T near to earth surface

Magnetic field is also called as Magnetic Induction or Magnetic Flux Density.

Ampere’s Swimming Rule

According to this rule, if we imagine a man swimming along current direction in wire such that current enters from feet and leaves from the head, then the N-pole deflected towards his left hand. 

Oersted's Experiment

Take a magnetic needle NS, which can rotate freely about a vertical axis in horizontal plane. Hold a conducting wire AB over the magnetic needle NS parallel to it. Complete the circuit by closing the key such that current flows from A to B.

It is found that N-pole of the magnetic needle gets deflected the west. If the direction of current in the wire is reversed (i.e. from B to A), the N-pole of magnetic needle gets deflected towards east. Since magnetic needle can be deflected by another magnetic field therefore current in the wire must be producing a magnetic field in the surrounding space.

Introduction - Magnetic Field

If a charge q is placed at rest at a point P near a metallic wire carrying a current I, it experience almost no force. We conclude that there s no appreciable electric field at the point P. This is expected because in any volume of wire (which contains several thousand atoms) there are equal amount of positive and negative charges. The wire is electrically neutral and does not produce an electric field.

(In fact, there is small charge density on the surface of the wire which does produce an electric field near the wire. This field is very small and can be neglected.)

However, if the charge q is projected from point P in the direction of current, it is deflected towards the wire (q is assume to be positive). There must be a field which exerts a force on charge when it is projected, but not when it is kept at rest. This field is called Magnetic Field.

The branch of physics which deals with the magnetism due to electric current is called electromagnetism.

Some result of experiments for the magnetic field due to a straight long current-carrying wires are shown below. The wire is perpendicular to the plane of the paper. A ring of compass needles surrounds the wire. The orientation of the needles is shown when

Maximum Power Transfer Theorem

It states that the power output across the load due to a cell or battery, is maximum if the load resistance is   equal to the effective internal resistance of a cell or battery. 

Some Effect of Heating Effect of Currents

The wires supplying current to an electric lamp are not practically heated while that of the filament of lamp becomes white hot. Wire has very less resistance but filament has higher resistance. Heating is proportional to R.

Nichrome wire (alloy of Ni and Cr): it has high melting point and high value of specific resistance.

            ii. It can be easily drawn

            iii. It is not oxidized easily when heated in air

Resistance of high electric power instruments is smaller than that of low electric power.

Fuse wire is generally prepared by tin-lead alloy. It should have high resistivity, low melting point and of suitable current rating. Fuse wire is used in series with electrical installation.

Efficiency of an electric device (η)

                                    η = output power/input power

      For electric motor,   η = output mechanical power/input electric power, input electric power =output mechanical power + power lost in heat.

Electric Energy

The electric energy consumed in a circuit is defined as the total work done in maintaining the current in an electric circuit for a given time.

Electric Energy =VIt=I²Rt= V²/Rt=P.t

SI unit is Joule, also 1 joule = watt-second

Commercial unit of electric energy is kilowatt hour (kWh) or Board of trade unit (B.O.T.U) or UNIT of electricity

1kWh=1000watt x 1 hours = 1000watt x 60min x 60s=3.6x10⁶ J

No. of units of electricity consumed = watt-hour/1000

Electric Power

The rate at which electric work is done by the source of emf in maintaining the current in electric circuit

W=VIt

Therefore Electric Power (P) = W/t =VIt/t=VI watt or joule/s

Power is said to be one watt if one ampere of current flows I it against a potential difference of 1 volt

Commercial unit of power is horse power, 1HP=746watt

P=VI=I²R=V²/R

It is the chemical energy of cell which supplies the power to the circuit.

Heat Produced by electric Current

Consider a conductor of resistance R, potential difference across it V and I is current flowing for some time t.

Total charge flow from one end to other q = It. Also work done in carry a charge from one end to other of conductor is

W=Potential difference x charge = Vq = VIt =I²Rt joules.

I²Rt is called electric work done which appears as heat.

H=W= I²Rt joules = I²Rt/4.18 calories.

Joule heating effect is irreversible. If direction of current changed it will not produce cooling but heat only.

Heating effects of Current: Joule's Effect

Whenever electric current passed through a conductor, it becomes hot after a certain time. This effect of getting hot by conductor is called as heating effect of current; Joule’s Law.

Amount of heat produced (H) when a current I flows through a conductor of resistance R for a time t is given by

           H α I²Rt …… known as joule’s law of heating.

When potential difference is applied across the conductor, E produced due to this potential exerts the force on electrons. Electrons gain kinetic energy and loss it when collide in between. This lost energy rise the temperature of the ion or atoms. Hence temperature of conductor increased.

E.m.f. of cell converts into the heat energy of conductor.