**Problem : **

Two wires run parallel to each other, each with a current of **10 ^{9}** esu/sec. If
each wire is 100 cm long, and the two wires are separated by a distance of 1 cm,
what is the force between the wires?

This is the simplest case of magnetic interaction between currents, and we simply plug in values to our equation:

**Problem : **

Three wires, each with a current of ** i**, run parallel and go through three corners
of a square with sides of length

Three wires run a current into the page. What is the magnetic field at point
*P*?

To find the net magnetic field, we must simply find the vector sum of the contributions of each wire. The wires on the corners contribute a magnetic field of the same magnitude but are perpendicular to each other. The magnitude of each is:

The fields from each wire at point *P*

B_{x} | = | - B_{2} - B_{3}sin 45^{o} = - - = - | |

B_{y} | = | - B_{1} - b_{3}sin 45^{o} = - - = - |

Notice from the symmetry of the problem that the

**Problem : **

Compass needles are placed at four points surrounding a current carrying wire, as shown below. In what direction does each needle point?

Compass needles are placed at four points in a plane perpendicular to the
wire.

Compasses in the presence of a magnetic field will always point in the direction of the field lines. Using the right hand rule we see that the field lines flow counterclockwise, as seen from above. Thus the compasses will point as such:

The direction of the four compasses placed around a current-carrying wire

**Problem : **

What is the force felt by a particle with charge ** q** travelling parallel to a wire
with current

We have derived the force felt by another wire, but have not derived it for a
single particle. Clearly the force will be attractive, as the single charge can
be seen as a "mini current" running parallel to the wire. We know that
** B = **, and that

**Problem : **

Two parallel wires, both with a current *I* and length *l*, are separated by a
distance ** r**. A spring with constant

Two wires, one connected to a spring, shown before the spring is stretched to
the force between the wires.

The spring will reach its maximum displacement when the force exerted by one
wire on the other is in equilibrium with the restoring force of the spring. At
its maximum displacement, ** x**, the distance between the two wires is approximated
by

= | kx | ||

x | = |

Although we did use an approximation to find the answer, this method is a useful way of determining the strength of the magnetic force between two wires.

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