Conceptual Physics

Use the relationship between field strength, potential difference and distance in a
uniform electric field to rewrite E, and then solve for the potential difference
between the ends of the wire segment.

Physics principles and equations The strength of the force exerted by a magnetic field on a charge moving perpendicular to it is

We will also use the definition of an electric field.

The equation that relates potential difference to electric field strength and distance in a uniform electric field is

In this case, the distance d is the wire length L. Step-by-step derivation

We employ the strategy and equations mentioned above and use algebra to solve for the potential difference.

As the equation indicates, longer wires, higher velocities, and stronger magnetic fields lead to greater induced potential differences. This derivation considered the case of motion perpendicular to the magnetic field. If the motion were not perpendicular, we would use trigonometry to determine the component of the motion that was perpendicular to the field. In general, we would conclude that ǻV = LvB sin ș, just as the magnetic force equalsqvB sin ș.

Potential difference across wire

segment

For motion perpendicular to field:

ǻV = LvB

ǻV = potential difference across wire

L = length of wire

v = speed

B = magnetic field strength

Step Reason

1. FB = FE forces in equilibrium

2. qvB = Eq substitute expressions for forces

3. vB = E divide by q

4. solve given equation for E

5. substitute equation 4 into equation 3

6. ǻV = LvB solve for ǻV

29.6 - Magnetic flux

Magnetic flux is analogous to electric flux. Specifically, magnetic flux is the product of a surface area with the component of a magnetic field passing perpendicularly through the surface, just as electric flux is the measure of how much electric field passes perpendicularly through a surface. The unit for magnetic flux is the weber (Wb). One weber is one tesla·m^2 , the units for magnetic field strength times those for area. With both electric and magnetic flux, the cosine of the angle between the field and the area vector is used to measure the component of the field passing perpendicularly through the surface. The area vector is normal to the surface and equal in magnitude to its area. In Equation 1, you see the equation for magnetic flux. It states that magnetic flux equals the dot product of the magnetic field and area vectors, which is calculated as the product of the magnetic field strength, the surface area, and the cosine of the angle ș. This angle is shown in the diagram. You will use the concept of magnetic flux, and changes in magnetic flux, to further your understanding of how changing magnetic fields induce emfs.

Magnetic flux

Amount of field passing through surface Depends on: ·Field strength at surface ·Amount of surface area ·Angle between field, area vector