Physics – Goyals Academy

Magnetic Force

If a charged particle is projected in a magnetic field, 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 predicted 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.

Sensitiveness of Potentiometer

Sensitiveness of Potentiometer means is the smallest potential difference can be measured with the help of Potentiometer.

Sensitivity of Potentiometer can be increased by decreasing its potential gradient. The same can be achieved by

1. By increasing the length of potentiometer wire.

2. If the potentiometer wire is a fixed length, the potential gradient can be deceased by reducing the current in the potentiometer wire circuit with help of rheostat.

Magnetic Dipole

Magnetic dipole consists to two unlike poles of equal strength and separated by a small distance.
The distance between the two poles of the bar is called magnetic length of the magnet. It is a vector directed from S-pole to N-Pole and represented by 2l.

Magnetic dipole is the product of the strength of either dipole (m) or the magnetic length (2l) of the magnet. It is represented by M.

It is vector quantity directed from South to North Poles.
SI unit of M is ampere-meter2 or joule/tesla.

Current Loop as a Magnetic Dipole

A current loop act as a magnetic dipole as it has both south and north pole.

Current loop act as Magnetic dipole

When we see a current carrying loop from top, current direction is anticlockwise and has north polarity. If, lower face of loop is seen from bottom then current direction is clockwise and have south polarity. Overall it behaves as a magnetic dipole depends upon

Physical Significance Of Dipoles

Physical significance of dipole is that it is used to predict whether a molecule is polar or non polar.

In most molecules, the centre’s of positive charges and of negative charges lie at the same place. Therefore, their dipole moment is zero and that molecule is considered as non polar.

CO2 and CH4 are of this type of molecules. However, they develop a dipole moment when an electric field is applied.

But in some molecules, the centres of negative charges and of positive charges do not coincide. Therefore they have a permanent electric dipole moment, even in the absence of an electric field. Such molecules are called polar molecules.

A water molecule, H2O, is an example of this type

Electric Dipole

An electric dipole is a pair of equal and opposite point charges q and –q, separated by a distance 2a. The line connecting the two charges defines a direction in space.

i.e. p = q × 2a

By convention, the direction from –q to q is said to be the direction of the dipole. The mid-point of locations of –q and q is called the centre of the dipole.

The total charge of the electric dipole is obviously zero as it contains two equal and opposite charge which cancels each other . This does not mean that the field of the electric dipole is zero.

The electric field due to a dipole falls off, at large distance, faster than like 1/r2 (the dependence on rof the field due to a single charge q).

The electric field produced by a dipole is known as dipole field.

Properties of Electric Field Lines

An electric field line is, in general is the path followed by a +ve charge when kept in an electric field.

An arrow on the curve is obviously necessary to specify the direction of electric field from the two possible directions indicated by a tangent to the curve. A field line is a space curve, i.e., a curve in three dimensions.

Properties of Electric field lines: –

1. The electric lines of force are imaginary lines.

2. A unit positive charge placed in the electric field tends to follow a path along the field line if it is free to do so.

3. The electric lines of force came out from a positive charge and came in a negative charge.

4. The tangent to an electric field line at any point gives the direction of the electric field at that point.

5. Two electric lines of force can never cross each other.Because If they do, then at the point of intersection, there will be two tangents. It means there are two values of the electric field at that point, which is not possible.

Further, electric field being a vector quantity, there can be only one resultant field at the given point, represented by one tangent at the given point for the given line of force.

6. Electric lines of force are closer (crowded) where the electric field is stronger and the lines spread out where the electric field is weaker.

7. Electric lines of force are perpendicular to the surface of a positively or negatively charged body.

8. Electric lines of force contract lengthwise to represent attraction between two unlike charges.

9. Electric lines of force exert lateral (sideways) pressure to represent repulsion between two like charges.

10.The number of lines per unit cross – sectional area perpendicular to the field lines (i.e. density of lines of force) is directly proportional to the magnitude of the intensity of electric field in that region.

11. Electric lines of force do not pass through a conductor. Hence, the interior of the conductor is free from the influence of the electric field.

i.e. E in a conductor is 0

12. Electric lines of force can pass through an insulator.

Difference between potentiometer and voltmeter

Potentiometer	Voltmeter
Potentiometer measure emf of cell very accurately.	Voltmeter measure emf of cell approximately.
Potentiometer does not draw any current from known emf source while measuring current.	Voltmeter draw current from known emf source while measuring current.
While measuring emf, resistance of potentiometer become infinite.	While measuring emf, resistance of voltmeter becomes very high but measurable.
In the potentiometer sensitivity is high.	In the voltmeter sensitivity is low.
It is based on null deflection method.	It is based on deflection method

Basic Properties of Charge

If the sizes of charged bodies are very small as compared to the distances between them, we treat them as point charges. All the charge content of the body is assumed to be concentrated at one point in space. Some other properties of the electric charge are

1. Additive of charges :-
If a system contains n charges q1, q2, q3, …, qn, then the total charge of the system is q1 + q2 + q3 + … + qn .
Charge has magnitude but no direction. Proper signs have to be used while adding the charges in a system.

2. Charge is conserved :-
It is not possible to create or destroy net charge carried by any isolated system.
Sometimes nature creates charged particles: a neutron turns into a proton and an electron. The proton and electron thus created have equal and opposite charges and the total charge is zero before and after the creation.

3. Quantization of charge :-
Charges are integral multiples of a basic unit of charge denoted by e. Thus charge q on a body is always given by q = ne. where n is any integer, positive or negative.
By convention, the charge on an electron is taken to be negative; therefore charge on an electron is written as –e and that on a proton as +e. The fact that electric charge is always an integral multiple of e is termed asquantization of charge.

In the International System (SI) of Units, a unit of charge is called a coulomb and is denoted by the symbol C.In this system, the value of the basic unit of charge is e = 1.6 × 10–19 C

4. Charge can be destroyed: –
In some reactions like electron-positron annihilation charge can be destroyed .
Electron–positron annihilation occurs when an electron (e−) and a positron (e+
, the electron’s antiparticle) collide. The result of the collision at low energies is the annihilation of the electron and positron, and the creation of gamma ray photons:
e− + e+ → γ + γ
In this reaction, The net charge before and after is zero.

5. Charge can be created :-
In some reactions like pair production charge can be created .
Pair production is the creation of an elementary particle and its antiparticle.

γ → e− + e+
In this reaction, The net charge before and after is zero.

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. As Heating is proportional to R.
Nichrome wire (alloy of Ni and Cr) is used as :
i. It has high melting point and high value of specific resistance.
ii. It can be easily drawn into wire.
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

Output power is always less than that of input power because some energy lost in the form of heat and other forms of energy.