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# Force Between Two Parallel Wires: Ampere Definition

"A fact is a simple statement that everyone believes. It is innocent, unless found guilty. A hypothesis is a novel suggestion that no one wants to believe. It is guilty, until found effective"
Edward Teller

- 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, i1 exerts 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"

> Proof:

What do you call a dinosaur with an extensive vocabulary ? A thesaurus.

Dr. C. L. Davis
Physics Department
University of Louisville
email: c.l.davis@louisville.edu