Supplementary Notes for PHYS 212: Spring 212
Electric Potential, Work, Electric Potential Energy:
About Electric Field:
Electric field of a point-like charge (a charge that doesn’t have structure, a proton or an electron is a good approximation, whereas a charged sphere is the opposite example which is not a point-like.) at a field point P which is located at a point r distance away from the point charge is
Note that there is nothing, no charge, at the field point.
This electric field can be assigned to any point around
any charge distribution (in this case Q is the charge
distribution). Electric field’s direction
is along the line joining the field point to the source
of the field (i.e. Q in this case), and directed away
from the positive charge, and into the negative charge.
The picture depicts the positions and relative
magnitudes of the two electric fields. E total
represents the addition of two electric field
vectors ( E+q and E-q). Note that positive charges
field is smaller than that of the negative’s due
to different distances.
Another charge Q when placed at the
field point experiences a Coulomb force
From the +q and –q, which can be calculated as
This is a general formula that holds for any electric field (whereas kq/r2 holds for point charge only). Also if Q is positive, F’s direction is the same as E’s. If Q is positive, F’s direction is opposite to that of the E’s.
charge is opposite to that on the negative
charge even though both charges are placed
in the same electric field E.
Here PE is measured in Joules (J) and Potential V is measured in Volts (V).
When a charged particle follows the two paths (dotted lines above) depicted in the picture above, the work done by the field is the same for both of the paths. In addition, if a negative charge, say an electron (charge –e) is carried from A to B, work done by the electric field is negative. Because
work along AC is zero since force is
perpendicular to path. Work along
CD is qEd, where d is the distance
Electric Potential of Point-like Charges:
Note that, the sign of the charge should
be included in all of your calculations that
involve PE, V or W. The distance in
the above formula (r’s) are absolute values,
that is they are positive.
A negative charges electric potential will
be negative. Potential doesn’t depend on
The picture depict the electric field
lines as well as equipotential lines
for a positive point like charge. The
value of the potential for each line can be
calculated from the formula given above.
· A charge can freely be moves on an equipotential line or surface. This is because, on an equipotential line or surface ΔV = 0, therefore, W =-q ΔV = 0. It means that the work done by the electric field when a charge moves on an equipotential line/surface is zero.
· Electric field lines are perpendicular to the equipotential lines/surfaces.
· A conductor’s surface is an equipotential surface. This means that if a conductor is connected to a battery of 1.5 V at one point, all the points of the conductor at the potential of 1.5 V with respect to some reference point.