force on a current carrying conductor ? force between two parallel conductors in free space ? definition of ampere ? torque on a current carrying loop in a magnetic induction
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We have just seen that a long straight wire carrying current i1 produces a B field which forms concentric circles around the wire whose magnitude a distance "d" from the wire is given by

with direction given by "the" right-hand-rule.
If a second parallel wire carrying a current i2 is placed a distance "d" from the first, it will feel a force due to the presense of B1. The force felt by a length l2 of this second wire is

so that

with a direction such that i2 is attracted towards i1 as shown at right.
Then the force per unit length on i2 is given by

 Note that if we reverse the roles of i1 and i2 we obtain the same expression for F1/l1 . That is, i1exerts a force on i2 and i2 exerts an equal, but opposite, force on i1 as expected from Newton's Third Law ("Action equals Reaction").
The above analysis applies for parallel currents - the two wires are attracted to each other. If one of the currents is reversed, so that the currents are "anti-parallel", the force per unit length is unchanged, but the force acting on each wire is reversed. In other words the wires are now repelled from each other.
 "Like currents are attractive, unlike currents are repelled". Note that this is opposite to the behavior of point electric charges
Definition of the Ampere
The unit of electric current, the Ampere, is defined using the force between parallel wires carrying current.
"The Ampere is that current which when flowing in two infinite parallel wires one metre apart produces a force between them of 2 x 10-7 N/m"

with direction given by "the" right-hand-rule.
If a second parallel wire carrying a current i2 is placed a distance "d" from the first, it will feel a force due to the presense of B1. The force felt by a length l2 of this second wire is

so that

with a direction such that i2 is attracted towards i1 as shown at right.
Then the force per unit length on i2 is given by

 Note that if we reverse the roles of i1 and i2 we obtain the same expression for F1/l1 . That is, i1exerts a force on i2 and i2 exerts an equal, but opposite, force on i1 as expected from Newton's Third Law ("Action equals Reaction").
The above analysis applies for parallel currents - the two wires are attracted to each other. If one of the currents is reversed, so that the currents are "anti-parallel", the force per unit length is unchanged, but the force acting on each wire is reversed. In other words the wires are now repelled from each other.
 "Like currents are attractive, unlike currents are repelled". Note that this is opposite to the behavior of point electric charges
Definition of the Ampere
The unit of electric current, the Ampere, is defined using the force between parallel wires carrying current.
"The Ampere is that current which when flowing in two infinite parallel wires one metre apart produces a force between them of 2 x 10-7 N/m"
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