# Magnetism Investigation

Magnetism Investigation

PURPOSE

To measure the magnetic force between two current-carrying conductors, and calculate the magnetic permability of free space.

WHAT'S THE POINT?

To see magnetic fields producing a force on a conductor which carries a current.

Cutnell and Johnson, Chapter 21, Sections 5 and 10.

INTRODUCTION AND THEORY:

When a current I passes through a long, straight conductor, a magnetic field B is created. According to Ampere's law, the magnitude of the field at a perpendicular distance d from the conductor is given by the relation.

mu * I

B = --------------

2 * pi * d

In SI units the magnetic field is measured in tesla when I is in amperes and d is in meters. The quantity mu is a constant known as the permeability of free space and has the assigned value of

-7 tesla * meter

mu = 4 * pi * 10 ------------- (1)

amp

It is assigned this value in order to maintain consistent units when the permittivity of free space has the value associated with Coulomb's law for the electrostatic force between charges, with the additional requirement that the square of the speed of light in a vacuum be given by

1

c = ------------------- (2)

sqrt(epsilon * mu)

where epsilon is the permeability of free space.

If a long, straight conductor carrying current I' is placed in a magnetic field of strength B, the conductor will experience a force whose magnitude on a length L of the conductor is given by

F = I' * L * B * sin(theta) (3)

where theta is the angle between the current and field directions. The force F has the units of newtons if B is measured in teslas, I' in amperes, and L in meters.

Now, if two long, parallel conductors carrying currents I and I' are separated by a distance d, each will experience a force due to the magnetic field set up by the other. Combining Eqns. 1 and 3 for the case of parallel wires (theta = 90 degrees), the following result is obtained:

mu * I * I' * L

F = ----------------- (4)

2 * pi * d

The forces exerted on the two conductors are equal in magnitude and oppositely directed, as required by Newton's Third Law. If the currents are in the same direction, the conductors experience an attractive force, while oppositely directed currents will produce a repulsive force. This equation is valid only for infinitely long conductors. However, if the separation d between the conductors is very much less than the length of either conductor, then the error in the equation is negligible. If the currents in the two conductors are equal (I = I'), then Eqn. 4 becomes

-7 2 L

F = 2 x 10 I ----- (5)

d

in which we have incorporated the assigned value mu. This last result is used to define the unit of current, the ampere. Formally,

`` one ampere is that current which, if present in each of two parallel conductors of infinite length and separated by a distance of one meter in a vacuum, causes each conductor to experience a force of exactly 2 x 10^(-7) newton per meter of length. ''

At the National Institute of Science and Technology, primary ...