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Physics II

Class Notes, 4/14/99


Coulomb's Law applies only to point charges.

The potential difference between two points A and B is the work per charge required to move a charge of from A to B.

Video File #01

For a point charge q, the potential difference between points A and B depends only on the distances of points A and B from q.

For a large number of point charges qi the potential at the point (x,y,z) is the sum of the potential differences k qi / ri, where ri is the distance of qi from (x,y,z).

Video File #02

The electric field a point is defined as the force per unit charge experience by a test charge at the point.

If a test charge qTest experiences a force F at a point A, then the electric field at that point is E = F / qTest.

As seen before the potential difference between two points A and B is obtained by adding up the work contributions Fperpendicular `ds for some path between A and B.

Video File #03

The electrostatic flux through close surface enclosing a charge Q is 4 `pi k Q.

 

If a uniform line charge density `lambda is distributed in a long straight line, then a cylinder of radius r whose axis is along the line and not near either end of the line distribution will experience flux of through only the curved side of the cylinder.

For a large plane region where charge density is `sigma, a rectangular box with cross-sectional area A will enclose charge `sigma A and thus experience flux 4 `pi k `sigma A.

Video File #04

For two plates with area A, with charge Q uniformly distributed over one and -Q over the other, we have charge densities `sigma = +- Q / A.

The voltage between the capacitor plates is easily found to be 4 `pi k Q/A * d.

Video File #05

If space between the plates of a capacitor is filled with a material whose molecules tend to align with electric field (a dielectric material), the result can be a reduction in the electric field between the plates for a given charge Q on the plates.

Video File #06

The figure below depicts a loop of area A rotating in a magnetic field B directed perpendicular to the axis of the loop.

  

The hand-held generator used for the experiments works by rapidly rotating a loop of wire between the poles of two magnets.

The generator can be represented by the 'source' region enclosed in within the red curve of the figure below.

This picture is represented as a voltage source in series with the resistance, as in the figure below.

Video File #07

A charge q moving at velocity v in the presence of the magnetic field B will experience a force q v B sin(`theta), where `theta is the angle between the velocity of the charge and the magnetic field.

  • The direction of the force will be perpendicular to both v and B, with its direction determine by the right-hand rule.
  • The vector form of this relationship is in terms of the cross product v X B: F = q * v X B

For a current in a wire, the total of all the q * v contributions from the drifting charges is equal to the product I * L of the current in the length of the wire, so when the magnetic field and the wire are perpendicular the force is F = I L B, with the direction of the force determine by the right-hand rule.

  • If the field and the wire are are not perpendicular then F = I L B sin(`theta), where `theta is the angle between the field and the wire.

The net forces on a current loop, when the loop is oriented so that the magnetic field direction is in the plane of the loop as indicated below, give rise to a torque about the axis of the loop.

  • Had the loop been or oriented perpendicular to the magnetic field the torque would have been 0.

Video File #08

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