ELECTRIC FIELD
PROBLEM SOLVING
SAMPLE # 1
What is the magnitude of the electric field E at a field
point 2.0m from a point charge q = 4.0 nC?
Diagram
q =4.0nC
ɛ = ?
2.0 m
Formula
E = 1/ 4π𝛜𝝷 ( q/ r^2 )
Substitution
E = 9.0 x 10^9 N m^2/C^2 ( 4.0 x 10^-9 C)/ (2.0m) ^2
= 9.0 N/C
Sample # 2
1. A point charge q = -8.0 nC is located at the origin. Find the electric-field
vector at the field point x = 1.2 m, y = -1.6 m.
Diagram q = -8.0 nC
X = 1.2 m
Y = -1.6 m
Formulas
For magnitude vector
r= √ x^2 + y^2
r= √ (1.2m)^2 + (-1.6m)^2
r= 2.0 m
Unit vector ( direction )
^r = r^/r = xi + yj/ r = (1.2m)i + ( -1.6m) j/ 2.o m = 0.60i -0.80j
E = 1/ 4π𝛜𝝷 ( q/ r^2 ) ^r
= 9.0 x 10^ 9 N m^2/ C^2 ( -8.0 x 10 ^-9 C ) / (2.0 m)^2 ( 0.60i -0.80j )
= (- 11N/C )i + (14N/C) j
Sample # 3
When the terminal of a battery are connected to two parallel conducting
plates with a small gap between them, the resulting charges on the plates
produce a nearly uniform electric field E between the plates. If the plates
are 1.0 cm apart and are connected to a 100-volt battery, the field is
vertically upward and has magnitude of E = 1.00 x 10^4 N/C. If the
electron e ( charge -e = -1.6o x 10^-19 C, mass 9.11 x 10^-31 Kg) is
released from rest at the upper plate, a)what is the acceleration? b) What
is the speed and kinetic energy does it acquire while travelling 1.0 cm to
the lower plate? c) How long does it take to travel this distance?
Diagram
a) ay = Fe/ m = -eE / m = ( -1.60x10^-19C) ( 1.00x10^4N/C)/ 9.11 x10^-31kg
= -1.76x10 ^15m/s^2
b)
vy = √ 2ayΔd = √ 2(-1.76x10 ^15m/s^2) ( -1.0 x 10^-2 m)
= -5.9 x 10^6 m/s
c)
K = ½ mv^2 = ½ ( 9.11x 10^-31 kg) ( -5.9 x 10^6 m/s) ^2
= 1.6 x 10 ^-17 J
d)
t= vy-voy/ ay = (-5.9 x 10^6 m/s) - 0 / -1.76x10 ^15m/s^2
= 3.4x10 ^-9 second
Field of an electric dipole
Point charges q1= +12nC and q2 = -12NC are 0.100 m apart ( see the diagram ) (
such pair of points charges with equal magnitude and opposite charges are called
electric dipoles.) Compute the electric field caused by q1, the field caused by q2
and the total field a) at point a b at point b and c) at point c.