Objective

Charges
• A proton and an electron each have this amount of charge, although the proton is positively
charged (q = +e) while the electron is negatively charged (q = −e). Even though the proton
and the electron share the same magnitude of charge, they do not share the same mass; the
proton has a much greater mass than the electron
.
• While opposite charges exert attractive forces, like charges those that have the same sign
exert repulsive forces.

• Most matter is electrically neutral, as a balance of positive and negative charges ensures a
relative degree of stability

• When charges are out of balance, the system can become electrically unstable. Even
materials that are normally electrically neutral can acquire a net charge as result of friction

• The SI unit of charge is the coulomb, and the fundamental unit of charge is e = 1.6 × 10−19 C
Charge on Insulator and Conductor

• An insulator will not easily distribute a charge over its surface and will not transfer that charge
to another neutral object very well—especially not to another insulator
• when a conductor is given a charge, the charges will distribute approximately evenly upon the
surface of the conductor. Conductors are able to transfer and transport charges and are often
used in circuits or electrochemical cells.
Quantization of Charge
Coulomb’s Law
Coulomb’s law quantifies the magnitude of the electrostatic force Fe between two point charges

where ,

F is the magnitude of the electrostatic force,

k is Coulomb’s constant,

q1 and q2 are the magnitudes of the two charges,

r is the distance between the charges.

Coulomb’s constant
Coulomb’s constant (also called the electrostatic constant) is a number that depends on the
units used in the Coulomb equation.

where ε0 represents the permittivity of free space and equal to

Qn: A positive charge is attracted to a negative charge a certain distance away. The charges are
then moved so that they are separated by twice the distance. How has the force of attraction
changed between them?
Qn:Negatively charged electrons are electrostatically attracted to positively charged protons. Because
electrons and protons have mass, they will be gravitationally attracted to each other as well. What is the
ratio of the electrostatic force to the gravitational force between an electron and proton?
Electric Field
 Electric field Intensity
Electric fields are produced by source charges ( Q). When a test charge (q) is placed in an
electric field (E), it will experience an electrostatic force (Fe) equal to qE.
Electric field intensity due to point charge
• If the charges are like charges (both positive or both negative), then the potential energy
will be positive. If the charges are unlike (one positive and the other negative), then the
potential energy will be negative.

The electric potential energy of a system will increase when two like charges move toward
each other or when two opposite charges move apart. Conversely, the electric potential
energy of a system will decrease when two like charges move apart or when two opposite
charges move toward each other.
Electric Potential
Electric potential is defined as the ratio of the magnitude of a charge’s electric
potential energy to the magnitude of the charge itself , where V is the electric
potential measured in volts (V)

Electric potential is a scalar quantity, and its sign is determined by the sign of
the source charge Q. For a positive source charge, V is positive, but for a
negative source charge, V is negative
• Electric potential is the ratio of the work done to move a test charge from
infinity to a point in an electric field surrounding a source charge divided by the
magnitude of the test charge.

where Wab is the work needed to move a test charge q through an electric field from point a to
point b.

• Wab must be negative, which represents a decrease in electric potential energy

Qn : If a charge of +2e and a charge of −3e are separated by a distance of 3 nm, what is the potential energy
of the system? (Note: e is the fundamental unit of charge equal to 1.6 × 10−19 C, and k is the electrostatic
constant )
Equipotential Lines
• An equipotential line is a line on which the potential at every point is the
same. That is, the potential difference between any two points on an
equipotential line is zero.

• From the equation for electrical potential, we can see that no work is done
when moving a test charge q from one point on an equipotential line to
another

• Work will be done in moving a test charge q from one line to another, but the
work depends only on the potential difference of the two lines and not on the
pathway taken between them
 Equipotential Surfaces

Potentials at different points are visualized

by equipotential surfaces (just like E-field
lines).

Just like topographic lines (lines of equal

elevations).

E-field lines and equipotential surfaces are

mutually perpendicular
Torque on Dipole
Electric Potential and Electric field due to Dipole
Qn:The H2O molecule has a dipole moment of 1.85 D. Calculate the electrical potential due to a
water molecule at a point 89 nm away along the axis of the dipole. (Note:1 D (debye) = 3.34 ×
10−30 C · m)
Magnetic field
Any moving charge, whether a single electron traveling through space or a
current through a conductive material, creates a magnetic field. The SI unit for
magnetic field strength is the tesla (T)
Infinitely long and straight current-carrying wire
Magnitude of the magnetic field produced by the current I in the wire at a perpendicular
distance, r, from the wire as-

where , B is the magnetic field at a distance r from the wire , µ0 is the permeability of
free space , I is Current flowing in the long straight wire
Permeability Constant (µ0)
The permeability constant (µ0), also known as the magnetic constant or the permeability of free
space, is a measure of the amount of resistance encountered when forming a magnetic field in a
classical vacuum. The magnetic constant has the exact (defined) value (µ0 = 4π × 10−7 H·m−1 )
Circular loop of current-carrying wire

For a circular loop of current-carrying wire of radius r, the magnitude of the magnetic field at
the center of the circular loop is
Qn:Suppose a wire is formed into a loop that carries a current of
0.25 A in a clockwise direction, as shown ,Determine the direction of
the magnetic field produced by this loop within the loop and outside
the loop. If the loop has a diameter of 1 m, what is the magnitude of
the magnetic field at the center of the loop?

Sol -
Magnetic Materials
• Diamagnetic materials are made of atoms with no unpaired electrons and that have no net
magnetic field.These materials are slightly repelled by a magnet and so can be called weakly
antimagnetic.
• Paramagnetic materials will become weakly magnetized in the presence of an external
magnetic field, aligning the magnetic dipoles of the material with the external field. Upon
removal of the external field, the thermal energy of the individual atoms will cause the
individual magnetic dipoles to reorient randomly. Some paramagnetic materials include
aluminum, copper, and gold
• Ferromagnetic materials, like paramagnetic materials, have unpaired electrons and
permanent atomic magnetic dipoles that are normally oriented randomly so that the material
has no net magnetic dipole. However, unlike paramagnetic materials, ferromagnetic
materials will become strongly magnetized when exposed to a magnetic field or under
certain temperatures. Common ferromagnetic materials include iron, nickel, and cobalt
• The atoms of both paramagnetic and ferromagnetic materials have unpaired electrons, so
these atoms do have a net magnetic dipole moment, but the atoms in these materials are
usually randomly oriented so that the material itself creates no net magnetic field
Magnetic Force

Magnetic fields exert forces only on other moving charges. That is, charges do not
“sense” their own fields; they only sense the field established by some external
charge or collection of charges
Force on a Moving Charge
When a charge moves in a magnetic field, a magnetic force may
be exerted on it

where q is the charge, v is the velocity, B is the

magnitude of the magnetic field, and θ is the smallest
angle between the velocity vector v and the magnetic
field vector B.
Qn:Suppose a proton is moving with a velocity of 15 m/s
toward the top of the page through a uniform magnetic field
of 3.0 T directed into the page, as shown here:What is the
magnitude and direction of the magnetic force on the
proton? Describe the motion that will result from this setup.
(Note: The charge of a proton is 1.60 × 10−19 C, and its
mass is 1.67 × 10−27 kg.)
Qn:Suppose a wire of length 2.0 m is conducting a current of 5.0 A toward the top of the page
and through a 30 gauss uniform magnetic field directed into the page. What is the magnitude
and direction of the magnetic force on the wire?
 Lorentz force.
charges often have both electrostatic and magnetic forces acting on them at the same
time; the sum of these electrostatic and magnetic forces is known as the Lorentz force.
Practice Qn -
1. the magnitude of the electric force F exerted on
charged particle R due to S is:

1. F/2
2. F.
3. 2F.
4. 4F.
1. F/2
2. F/4
3. 2F.
4. 4F.
4. If the electric field at a distance r away from charge Q is 36 N/C . what is the ratio of the
electric fields at r, 2r, and 3r?
5. A positive charge of +Q is fixed at point R a
distance d away from another positive charge
of +2Q fixed at point S. Point A is located
midway between the charges, and point B is a
distance d/2. from +2Q, as shown below. In
which direction will a positive charge move if
placed at point A and point B, respectively?
6. Two parallel conducting plates are separated by a distance d. One plate carries a
charge +Q and the other carries a charge −Q. The voltage between the plates is 12 V.
If a +2 μC charge is released from rest at the positive plate, how much kinetic energy
does it have when it reaches the negative plate?
1. 9F
2. 3F
3. F
4. F/9
1. It rotates to align with the new field.
2. It accelerates linearly along the field lines.
3. It experiences no rotational or linear movement.
4. It both rotates to align with the new field and
accelerates linearly along the field lines.