Derive an expression for force acting per unit length between two parallel straight wires carrying current.
Answers
Answer:
F l = μ 0 I 1 I 2 2 π r. F / l is the force per unit length between two parallel currents I1 and I2 separated by a distance r. The force is attractive if the currents are in the same direction and repulsive if they are in opposite.
Answer:Force per unit length between two long straight parallel conductors: Suppose two long thin straight conductors (or wires) PQ and RS are placed parallel to each other in vacuum (or air) carrying currents I1 and I2 respectively. It has been observed experimentally that when the currents in the wire are in the same direction, they experience an attractive force (fig. a) and when they carry currents in opposite directions, they experience a repulsive force (fig. b). Let the conductors PQ and RS carry currents I1 and I2 in same direction and placed at separation r
B
1
=
2πr
μ
0
I
1
△F=B
1
I
2
△Lsin90
o
B
1
=
2πr
μ
0
I
1
I
2
△L
F=
2πr
μ
0
I
1
I
2
Σ△L=
2πr
μ
0
I
1
I
2
L
L
F
=
2πr
μ
0
I
1
I
2
N/m
Consider a current–element ‘ab’ of length ΔL of wire RS. The magnetic field produced by current-carrying conductor PQ at the location of other wire RS
According to Maxwell’s right hand rule or right hand palm rule no. 1, the direction of B1 will be perpendicular to the plane of paper and directed downward. Due to this magnetic field, each element of other wire experiences a force. The direction of current element is perpendicular to the magnetic field; therefore the magnetic force on element ab of length ΔL
Definition of Ampere: In S.I. system of fundamental unit of current ‘ampere' has been defined assuming the force between the two current carrying wires as standard. The force between two parallel current carrying conductors of separation r is
L
F
=
2πr
μ
0
I
1
I
2
N/m
f=
2π
μ
0
=2×10
−7
N/m
Thus 1 ampere is the current which when flowing in each of parallel conductors placed at separation 1m in vacuum exert a force of 2x10-7 on 1m length of either wire.