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Electric Fields
There are differences between field forces
and contact forces.
23.4 The Electric Field
2 0
2
0
r
Q
k q
F
E
r
q Q F k
e
e
- The electric field is the force on a small
charge, divided by the charge
- A positive test charge must be used
- SI unit N/C
F q E
q
F
E
e
e
0
0
- The force on a positive charge will be in the direction of the field; the force on a negative charge will be in the opposite direction.
- The electric field due to more than one point charge can be found using the principle of superposition:
“The electric field at any point is the vector sum of the fields at that point caused by each charge separately.”
Example 5
- Two point charges are located at the x – axis. Charge q 1 = +0.60 μC is located at x = 0 and charge q 2 = - 0.50 μC is located at x = 0.40 m. Point P is located at x = 1.20 m. What is the magnitude and direction of the electric field at P due to the two charges?
Example 23.
Electric Field Due to Two Charges
- A charge q 1 = +7.0 μC is
located at the origin, and a second charge q 2 = −5.0 μC is located on the x axis, 0.30 m from the origin. Find the electric field at point P , which has coordinates (0, 0.40) m.
Example 23.
Electric Field of a Dipole
- An electric dipole is defined as a positive charge q and a negative charge − q separated by a distance 2a. For the diploe shown in Figure 23.15, find the electric field E at P due to the dipole, where P is a distance y ≫ a from the origin.
23.5 Electric Field of a Continuous
Charge Distribution
- The electric field at due to one charge element carrying charge ∆𝑞 is - The total electric field at P due to all elements in the charge in the charge distribution is approximately
where the index i refers to the i th element in the distribution.
Example 23.
The Electric Field of a Uniform Ring of Charge
- A ring of radius a carries a uniformly distributed
positive total charge 𝑄. Calculate the electric field due to the ring at a point lying a distance x from the center along the central axis perpendicular to the plane of the ring.
Example 23.
The Electric Field of a Uniformly Charged Disk
- A disk of radius R has a uniform surface charge density . Calculate the electric field at a point P that lies along the central perpendicular axis of the disc and a distance x from the center of the disk.
23.6 Electric Field Lines
The electric field can be represented by field lines. These lines start on a positive charge and end on a negative charge.
An electric dipole is defined as a positive charge q and a negative charge − q separated by a distance 2a.
16_17.jpg
The electric field between two closely spaced, oppositely charged parallel plates is constant.
23.7 Motion of a Point Charge in
a Uniform Electric Field
- If the electric field is uniform
- If this is the only force acting on the point charge, then the net force is constant, and so is the acceleration:
F qE e
m
qE
m
F
a
- If the particle is moving in the direction of the
field, its motion will be a straight line; if its
motion has a component perpendicular to the
field, its motion will be the same as that of a
projectile.
- (+) acceleration in the direction of the field
- (-) acceleration in the direction opposite the
direction of the field
The Cathode Ray Tube
