DIRECTION and MAGNITUDE OF FORCE ON CURRENT CARRYING CONDUCTOR (X CBSE Physics)

DIRECTION OF FORCE ON CURRENT CARRYING CONDUCTOR:

The direction of force obtained by the Fleming’s left hand rule.  Stretch the forefinger, middle finger and the thumb of you left hand mutually perpendicular to each other as shown in figure. It the forefinger indicates the direction of the magnetic field and the middle finger indicates the direction of current, then the thumb will indicate the direction of motion (i.e., force) on the conductor.

Magnitude of Force :

Experimentally it is found that the magnitude of the force acting on a current carrying conductor kept in a magnetic field in direction perpendicular to it, depends on the following factors :

(i) The force F is directly proportional to the current flowing in the conductor, i.e. F 𝛂 I.

(ii) The force F is directly proportional to the intensity of magnetic field, i.e. F 𝛂 B.

(iii) The force F is directly proportional to the length of the conductor (inside the magnetic field), i.e. F 𝛂 l

Combining these we get, F 𝛂 I l B      or F = K I B l.

Where K is constant whose value depends on the choice of units. In S.I. units K = 1 and the unit of magnetic field is tesla (T). 1 tesla is equal to 1 Newton ampere^-1 metre^-1 or 1 Weber metre^-2.

Force is directly proportional to sin q where q is the angle between current and the direction of magnetic field. i.e. F 𝛂 sinϴ

Combining all we have F = BI l sinϴ .

Special cases:

(i) When  ϴ = 0° or 180° then, sinϴ = 0 so that F = 0. Force on a current - carrying conductor placed parallel to field is zero.

(ii) If ϴ = 90°, sin 90⁰ = 1, F = B l I is the maximum force. Force experienced by the conductor is the maximum when it placed perpendicular to magnetic field.

(iii) If  B = 0, F = 0 i.e. the coil placed in field free area doesn’t experience any force.

A moving charge in a magnetic field (direction of motion not parallel to the field direction) experiences a force called Lorentz force. Since current is due to flow of charge, therefore a conductor carrying current will experience a force.

The force acting on a current - carrying conductor placed in a magnetic field is: F = B I l

Now, if a charge Q flows in time t then the current    

So, writing in place of I in the above equation, we get:

Suppose the particle carrying the charge Q travels a length l in time t. Then the velocity v of the charged particle will be equal to l/t.

Writing v in place of l/t  in the above equation, we get :

Force on moving charge, F = B × Q × v

Where B = Magnitude of magnetic field, Q = Charge on the moving particle and v = Velocity of the charged particle (in metre per second).