Physics
Physics
Physics
Potential energy is energy which results from position or configuration. An object may
have the capacity for doing work as a result of its position in a gravitational field
(gravitational potential energy), an electric field (electric potential energy), or a
magnetic field (magnetic potential energy). It may have elastic potential energy as a
result of a stretched spring or other elastic deformation.
The difference in the potential energy ΔU of the system is equal to the negative
of the work done by the force
Like potential energy, the electric potential is a scalar. Usually we will refer to
electric potential simply as “potential”.
The general expression for the electric potential as a result of a point charge q can
be obtained by referencing to a zero of potential at infinity. The expression for
the potential difference is:
ELECTRIC POTENTIAL
The potential near an isolated +ve charge is positive. If we move a +ve test charge from
infinity to that point, the charge would move from a location where V=0 to a location
where V > 0. Thus ΔV > 0 same as ΔU > 0. And for isolated –ve charge the potential is –
ve.
If potential is zero at a point, no net work is done by the electric force as the test charge
moves in from infinity to that point, although the test charge may pass through region
where it experiences attractive or repulsive electric forces.
A potential of zero at a point does not necessarily mean that the electric force is zero at that
point
1 Volt = 1 joule/coulomb
Electron Volts
U=qV, units are usually Joules
Sometimes (especially in Atomic Physics) it is useful to express the energy in units of
electrons*Volts.
1 eV = Charge on electron * 1 Volt
1eV = 1.602 × 10-19 Joules
The energy required to move an electron or proton through a potential of 1V
CALCULATING THE POTENTIAL
FROM THE FIELD
An alpha particle (q=+2e) in a nuclear accelerator moves from one terminal at a potential
of Va= +6.5 × 106 V to another at a potential of Vb = 0. (a) What is the corresponding
change in the potential energy of the system?
(b) Assuming that the terminal and their charges do not move and that no external forces
act on the system, what is the change in kinetic energy of the particle?
ΔU = Ub – Ua = q(Vb-Va)
ΔU = -2.1 × 10-12 J
ΔK = - ΔU = 2.1 × 10-12 J
POTENTIAL DUE TO POINT
CHARGES
From above equation we can see that potential due to electric dipole is inversely
proportional to r2 not ad 1/r which is the case for potential due to single charge.
Potential due to electric dipole does not only depends on r but also depends on angle
between position vector r and dipole moment p.(e.g. V =0, θ=90)
ELECTRIC POTENTIAL DUE OF
CONTINUOUS CHARGE DISTRIBUTION
The electric potential (voltage) at any point in space produced by a continuous charge
distribution can be calculated from the point charge expression by integration since voltage
is a scalar quantity. Thus we do not encounter the difficulties that arose due to differing
directions of force elements dE or fiedl element s dE from different charge elements dq.
A Ring of Charge
Figure given below shows a uniform ring of positive charge. The contribution to the
potential at point P on its axis due to charge element dq = λ ds = λ R dφ is;
CALCULATING THE FIELD FROM THE
POTENTIAL
This is a fundamental connection b/w electric field and potential. Electric field is
the negative of the change in potential with distance. If ΔV is positive, the electric
field gives a force that opposes the movement of the positively charged test particle
from a to b. If ΔV is negative, the field gives a force in the direction of motion.
CALCULATING THE FIELD FROM THE
POTENTIAL
The work done by electric field along cb is zero, b/c the potential does not change
(ΔV = -W/q0). The work done along ac is Fx Δx = q0E Δx. Because the change in
potential energy is independent of path, we have again W = - ΔU
q0E Δx = -q0 ΔV
CALCULATING THE FIELD FROM THE
POTENTIAL
For an isolated charged conductor we know that; the electric field is zero in its interior
and the charge reside on the outer surface of the conductor.
If the charges are in equilibrium on the surface of the conductor, then its surface must
be an equipotential. If this were not so, some parts of the surface would be at higher
or lower potential than the other parts. However this contradicts our assertion that the
charges are in equilibrium and therefore, the surface must be an equipotential.
In electrostatic case, the entire conductor is at the same potential. However when
current flowing through conductors, a potential difference can exist b/w different
point in the conductor.
Note that we have made no assumptions about the shape of the conductor. If
conductor is spherical, the charge is uniformly distributed over the surface .
For conductors whose shape is non-spherical, the charge density is not
uniform over the surface, but the surface is still an equipotential.
The field and potential for an isolated charged spherical conductor; the field
is zero for r < R and decrease like 1/r2 for r > R.
The potential is constant for r < R and falls off like 1/r for r > R
POTENTIAL OF A CHARGED
CONDUCTOR