(iii)
Force between two parallel current carrying conductors and definition of ampere
Experimentally it has been observed that two current carrying conductors attract each other
when the currents in them are in same direction and repel each other when these are in opposite
directions.
P
S
P
S
Q
T
Q
T
I1
I2
I1
R
X
I2
R
Y
X
Y
Suppose X and Y are two long parallel straight conductors with currents I1 and I2 amp.

respectively. The magnitude of the magnetic field B , at any point on Y due to the current I1 in
X is given by
0 I1
B1 = 2 R
Perpendicular to plane of the page directed downward.

Hence current carrying conductor Y is thus situated in a magnetic field B1 perpendicular
to its length. Hence it experiences a magnetic force, magnitude of which is given by
F = I2 B1l
 0 I1 
= I2 
l
 2R 
and force per unit length
F 0 I1I 2

l 2 R
according to Fleming left hand rule the direction of this force is towards X when I1 & I2
are in same direction and is away from X when I1 & I2 are in opposite direction.
Similarly force per unit length of X due to current in Y is
 0 I1I 2
, directed opposite to
2 R
forces on Y due to X.
The directions of the forces on the two conductors show that the conductors attract each
other if currents are in same direction and repel each other if currents are in opposite direction.
If
I1 = I2 = I
so
F
 I2
= 0
l
2 R
F
 2  107 N/m , then the current
l
is said to be one ampere. So one ampere is that current which can produce a force of
2 × 10-7 N/m in vacuum between two infinitely long conductors placed 1 meter apart.
If now the value of current is such that when R = 1 m,
So
so
2  10
7
2
N
 0 1A 
=
m
2 1m
Wb 
0
7 N 
 107
= 10
2 
A  m 
A 
4