# Magnetic force on a current carrying wire virtual experiment

#### Quiz

Q1) The force on a moving charge in the presence of a magnetic field is always

A. Perpendicular to both the charge's velocity and the magnetic field
B. Parallel to the charge's velocity
C. Parallel to the magnetic field
D. None of the above

Q2)  A current is moving from north to south through a long wire that is lying horizontally on a table. What is the direction of the magnetic force if the magnetic field is directed up and out of the table?

A. toward the north
B. toward the east
C. toward the south
D. toward the west

#### Magnetic force on a current carrying wire Simulation(Virtual Experiment)

When the next simulation is not visible, please refer to the following link.

Magnetic force on a current carrying wire
If a magnetic field exerts a force on a single charged particle when it moves through a magnetic field, it should be no surprise that magnetic forces are exerted on a current-carrying wire as well (see Fig. 1). Because the current is a collection of many charged particles in motion, the resultant force on the wire is due to the sum of the individual forces on the charged particles. The force on the particles is transmitted to the “bulk” of the wire through collisions with the atoms making up the wire.

FIGURE 1 This apparatus demonstrates the force on a current carrying wire in an external magnetic field. Why does the bar swing away from the magnet after the switch is closed?

Some explanation is in order concerning notation in many of the figures. To indicate the direction of $\ B$, we use the following conventions:

 If $\ B$ is directed into the page, as in Figure 2, we use a series of green crosses, representing the tails of arrows. If $\ B$ is directed out of the page, we use a series of green dots, representing the tips of arrows. If $\ B$ lies in the plane of the page, we use a series of green field lines with arrowheads.

The force on a current-carrying conductor can be demonstrated by hanging a wire between the poles of a magnet, as in Figure 2. In this figure, the magnetic field is directed into the page and covers the region within the shaded area. The wire deflects to the right or left when it carries a current.

FIGURE 2  A segment of a flexible vertical wire partially stretched between the poles of a magnet, with the field (green crosses) directed into the page. (a) When there is no current in the wire, it remains vertical. (b) When the current is upward, the wire deflects to the left. (c) When the current is downward, the wire deflects to the right.

Magnetic Force on a wire resulting from a magnetic field
It is possible to determine the force of magnetism exerted on a current-carrying wire passing through a magnetic field at right angles to the wire. Experiments show that the magnitude of the force, $\ F$, on the wire, is proportional to the strength of the field, $\ B$, the current, $\ I$, in the wire, and the length, $\ L$, of the wire in the magnetic field. The relationship of these four factors is as follows:

 Magnetic Force on a Current-Carrying Wire in a Magnetic Field  $\ F=BIL$ The force on a current-carrying wire in a magnetic field is equal to the product of magnetic field strength, the current, and the length of the wire.

The strength of a magnetic field, $\ B$, is measured in teslas, T. 1T is equivalent to 1 N/A m.
Note that if the wire is not perpendicular to the magnetic field, a factor of $\sin \theta$ is introduced in the above equation, resulting in $\ F=BILsin \theta$ . As the wire becomes parallel to the magnetic field, the angle becomes zero, and the force is reduced to zero. When $\theta$=90°, the equation is again $\ F=BIL$.

Determining the Magnetic force’s direction
Faraday’s description of the force on a current-carrying wire does not completely describe the direction because the force can be upward or downward. The direction of the force on a current carrying wire in a magnetic field can be found by using the third right-hand rule. This technique is illustrated in Figure 3. The magnetic field is represented by the symbol B, and its direction is represented by a series of arrows. To use the third right-hand rule, point the fingers of your right hand in the direction of the magnetic field, and point your thumb in the direction of the conventional (positive) current in the wire.

Figure 3 The third right-hand rule can be used to determine the direction of force when the current and magnetic field are known.

The palm of your hand will be facing in the direction of the force acting on the wire. When drawing a directional arrow that is into or out of the page, direction is indicated with crosses and dots, respectively. Think of the crosses as the tail feathers of the arrow, and the dots as the arrowhead.