Electromagnetism - Current Carrying Conductors

Current Carrying Conductors

Consider C₁ D₁ and C₂ D₂ two infinite long straight conductors carrying currents I₁ ad I₂ in the same directing they are held parallel to each other at a distance r apart in the plane of paper. The magnetic field is produce due to current through each conductor shown separately in and (b). Since each conductor is in the magnetic field produced by the other therefore each conductor experiences a force.

Magnetic field induction at a point p one conductor C₂ D₂ due to current I₁ passing through C₁ D₁ is given by  B₁ = μ₀ / 4 π ² I₁ / r             (1)

According to right hand rule the direction of magnetic field B₁ is perpendicular to the plane of paper directed inwards.

As the current carrying conductor C₂ D₂ lies in the magnetic field B1 (produced by the current through C₁D₁ therefore, the unit length of C₂ D₂ will experience a force given by 

F₂ = B₁ I₂ X 1 = B₁ I₂ 

Putting the value of B1 we have 

F₂ = μ₀ / 4 π ² I ₁ I₂ / r                                                                                (2) 

According to Fleming's left hand rule force on conductor C₂ D₂ acts in the place of the paper perpendicular to C₂ D₂ directed towards C₁ D₁ similarly it cane shown that the conductor C₁ D₁ also experiences a force given by eqn. (2) which acts into he lance of paper perpendicular to C₁ D₁ and directed towards C₂ D₂hence C₁ D₁ and C₂ D₂ attract each other. 

It means the two linear parallel conductors carrying currents in the same direction attract each other. The force experienced by the unit length of each conductor is given by (2) further it can be shown that if the current in conductor C₁D₁ and C₁ D₂ are in opposite directions they repel each other with the same force as given by eq. (2) 

Definition of ampere

Relation is used to define 1 ampere 

Let I₁ = I₂ = IA; r = 1 m 

Then F = μ₀ / 4π ²I₁ I₂ / r = 10^-7 x 2 x 1 x 1 / 1 

(∴ μ₀ / 4 π = 10^-7) = 2 x 10 ^-7 Nm ^{- 1} 

Thus one ampere is that much current which when flowing through each of the two parallel uniform long linear conductor placed in free space at a distance of one meter from each other will attract or repel each other with a force of 2 x 10^-7 N per meter of the length. 

Note if two liner current carrying conductors of unequal length are held parallel to each other then the force on long conductor is due short conductor and long conductors.

if I L = length of short and long conductor respectively.

I₁ I2 = current through short hang long conductor

R = separation between these two parallel conducts (i) then force on long conduct = force on short conductor = μ₀ / 4 π²I₁ I₂ / r.

(ii) The force on each conductor is same in magnitude and opposite in direction the force on two conductors obey Newton's third law of motion.

(b) When two currents approach a point or they go away from that point then they experience an attractive force. 

(c) When one current out of the two approaches a point and another one goes away from that point they then experience a force of repulsion. 

(d) When two charges of values q₁ and q₂ moving with velocities v₁ and v₂ on parallel straight paths distance r apart then the force acting between them is given by 
 
F = μ₀ / 4 π q₁ q₂ v₁ v₂ / r² 

Proof: When a charge q moving with velocity v for time dt covers a distance dl it will behave as a current element I dl where

Idl = q / dt dl = q dl / dt = qv

If I₁ I₂ are the currents corresponding to motion of charges q₁ and q₂ with velocity v₁ and v₂ then 

I₁ dl₁ = q₁ v and I₂ dl ₂ = q₂ v₂

The magnitude of magnetic force acting between these two parallel current elects distance r apart is given by 

Fm = μ₀ / 4π I₁ I₂ / r² dl₁ dl₂ or Fm = μ₀ q₁ q₂ / 4π r² v₁ v₂.

(e) A fixed horizontal wire A carrying current I₁ will support another horizontal wire B, carrying current I₂hanging in air at a distance r below the wire A if the direction of currents in the two wires is same here weight pr unit length of wire B is equal to the force of attraction acting per unit length of the wire B 

Mg μ₀ / 4π ²I₁ I₂ / r 

ExpertsMind.com - Current Carrying Conductors Assignment Help, Current Carrying Conductors Homework Help, Current Carrying Conductors Assignment Tutors, Current Carrying Conductors Solutions, Current Carrying Conductors Answers, Electromagnetism Assignment Tutors