Force Between Two Parallel Conductors
Case (i) Currents in the same direction.
In the figure given below are shown two parallel conductors P and Q carrying currents I1 and I2 amperes in the same direction i.e. upwards. The field strength in the space between the two conductors is decreased due to the two fields there being in opposition to each other. Hence, the resultant field is as shown in the figure. Obviously, the two conductors are attracted towards each other.
(ii) Currents in opposite directions.
If, as shown in the figure given above, the parallel conductors carry currents in opposite directions, then field strength is increased in the space between the two conductors due to the two fields being in the same direction there. Because of the lateral repulsion of the lines of the force, the two conductors experience a mutual force of repulsion as shown separately in Figure given below.
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Magnitude of Mutual Force
It is obvious that each of the two parallel conductors lies in the magnetic field of the other conductor. For example, conductor P lies in the magnetic field of Q and Q lies in the field of P. If ‘d’ metres is the distance between them, then flux density at Q due to P is [Art. Ampere’s Circuital Law]
If l is the length of conductor Q lying in this
flux density, then force
Obviously, conductor P will experience an equal force in the opposite direction. The above facts are known as Laws of Parallel Currents and may be stated as follows :
(i) Two parallel conductors attract each other if currents through them flow in the same direction and repel each other if the currents through them flow in the opposite directions.
(ii) The force between two such parallel conductors is proportional to the product of current strengths and to the length of the conductors considered and varies inversely as the distance between them.
Definition of Ampere:
If has been proved in the above article that the force between two infinitely long parallel currently- carrying conductors is given by the expression
The force per metre run of the conductors is
If I1 = I2 = 1 ampere (say) and d = 1 metre, then F = 2 × 10−7 N
Hence, we can define one ampere current as that
Current which when flowing in each of the two infinitely long parallel conductors situated in vacuum and separated 1 metre between centres, produces on each conductor a force of 2 × 10−7 N per metre length
Read article – Units of Resistivity
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