PHYSICS

t1 cp = -f B Eds = - Ed (15.9)
A
or
E = _ t1cp
d
(15.10)
where the minus sign results from the fact that point B is at a
lower potential than point A.
With a non-uniform electric field, from the Equation (15.7)
we can express the potential difference (dcp) between two points a
distance (ds) apart as:
dcp = -E· ds (15.11)
If the electric field has only one component (E), then E-ds =
= Exdx. Therefore, Equation (15.7) becomes dip = - Exdx or:
dcp
Ex = - dx (15.12)
Therefore, the electric field is equal to the negative of the derivative
of the potential with respect to some coordinate.
In general, the electric potential is a function of all three spatial
coordinates. If cp (r) = cp (x,y,z) is given in the rectangular
coordinates, the electric field components are given by:
E = - dcp E = _ dcp E = _ dcp
x dX' Y dy' Z dZ (15.13)
F = qE = mii (15.14)
where m is the mass of the particle. The acceleration of the
particle is therefore given by:
a = qE (15.15)
m
15.2.7. Oscillograph
The oscillograph is an electronic instrument widely used in
making electrical measurements when rapidly changing electrical
signals are studied, e.g. nerve action potentials or electrical
signals in plants. The main component of the oscillograph is the
cathode ray tube (CRT), shown in fig. 15.3. The mode of operation
Fluorescent screen
Fig. 15.3. The cathode ray tube: 1 - heater; 2 - cathode;
3 - control grid; 4 - focusing anode; 5 - accelerating anode;
6 - plates for horizontal deflection; 7 - plates for vertical deflection
In these expressions, the derivatives are called partial derivatives.
From this, it follows that the unit of electric field (Nlc)
can be also be expressed as volts per meter (Vim).
Any surface consisting of a continuous distribution of points
having the same potential is called an equipotential surface.
Equipotential surfaces are always perpendicular to the electric
field lines.
15.2.6. Motion of Charged Particles in an Uniform Electric Field
When a particle of charge q is placed in an electric field (E), the
electric force on the charge is q E. If this is the only force exerted on
the charge, then Newton's second law applied to the charge gives:
of the CRT itself provides a simple example of the movement of
charges (electrons) under the influence of electric fields. The
whole interior of the tube is highly evacuated. The cathode is
raised to a high temperature by the heater and electrons (cathode
rays) evaporate from its surface. The accelerating anode is maintained
at a high positive potential relative to the cathode so that
there is an electric field directed between the anode and cathode.
The electrons passing through the hole in the anode travel with a
constant velocity from the anode to the fluorescent screen. The
complete cathode-anode assembly is called the electron gun. The
electrons then pass between two pairs of deflecting plates, the first
of which controls the horizontal deflection of the beam, the second
- the vertical deflection. The sweep speed is controlled by
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