12 Electrostatic Phenomena
Answers to Questions
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They acquire different types of charge. An experiment to test this could be; rub a piece of plastic with a silk
rag. Now hold each of these items, one at a time, near a light object (such as a pith ball) with known
charge. Note the behavior of the light object in each case.
a. Each pith ball will acquire a negative charge. In charging by contact, a pith ball will share some of
negative charge produced on the rod by rubbing.
b. Since both pith balls have the same sign of charge, they will repel one another.
The nylon cloth will acquire a negative charge, which means it has an excess of electrons after rubbing the
glass rod. Since the glass becomes positive and it is only the negatively charged electrons that are
transferable, after rubbing, some electrons which were originally on the glass will attach themselves to the
nylon.
a. The pith ball touched to the glass rod will acquire a positive charge and the one touched to the cloth will
gain a negative charge. Objects charged by contact acquire the charge on the contacting body.
b. Since they have opposite signs of charge, the two pith balls will attract one another.
No. They gain like charges. This is clear from the fact that the leaves spread apart rather than close up petallike as they would do if their charges were opposite in sign.
The leaves move closer together. This is because the rod has acquired opposite charges from the rubbing
process. The leaves acquired the same charge as the rod had and therefore, opposite the charge of the
fur.
The comb is expected to acquire a negative charge, like the case of rubbing a plastic rod with fur.
The single fluid model gave indications of surplus or dearth of the fluid. A surplus carried a positive amount
of the fluid; a dearth implied a negative amount. Rather than deal with the invisible fluid itself, one could
easily deal with the consequence of the fluid’s presence or lack in the object; that is, the positive charge
(indicating a surplus of fluid) or a negative charge (indicating a lack of fluid) or a neutral charge (indicating
neither too much nor too little fluid).
No. Glass is an insulator not a conductor. The electroscope will not discharge.
It will discharge. People are good conductors.
Charging by induction results in like charge. Therefore the charge on the ball will be negative, as is the
charge of the plastic rod.
No. The separated charges will return to their undisturbed positions. There will not be any nearby charge
imbalance to hold them in separation.
Yes. The bits of paper become polarized by the charged rod being brought close, with the sign of the charge
on the side of the bit of paper near the rod being opposite to the sign of charge on the rod.
The uncharged pith balls were attracted to the charges rod because unbalanced forces were induced on
the balls by the rod. When contact is made, the balls gain charge of the same sign as the rod.
Yes. The repulsive force between two charges produces a torque about the thin wire that supports the
beam causing the wire to twist. The twisting of the wire develops an elastic restoring torque that returns
the beam to its original position when one charge is removed.
Start with four insulated spheres, one with at least 16 units of charge, the others uncharged. Touch the
charged sphere to a second sphere. Both of these spheres now carry a charge of 8 units. Touch one of
these to an uncharged sphere. Now there are three charged spheres, one with eight units and two with four
units of charge each. Repeat, touching one of the four unit charge carries to the last uncharged sphere.
Now there are four charged spheres with units of charge eight, four, two, and two respectively.
No. Since the Coulomb force varies inversely as the square of the distance between the charges, doubling
the distance reduces the force by a factor of 1/4.
The force between the two charges will be quadrupled. The Coulomb force between the charges varies as the
product of the two charges. Doubling each gives a four-fold increase.
No. The force between charges can be either attractive or repulsive but the gravitational force between matter
is always attractive.
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Q21
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Yes. All that is required is that there exists a charge somewhere in the space so that it can exert a force on a
positive test charge brought to a given point.
The field at A is zero.
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No. The electric field lines that we can imagine emanating from the charge diverge with increasing distance
indicating a field that decreases in strength with distance.
Potential energy decreases. A positive charge that is free to move will go from higher to lower potential
energy, that is toward the negative charge.
The potential energy increases. Potential energy is the work against a conservative force. To move the
negative charge at constant velocity closer to the negative charge requires a force opposite the direction the
charge is moved.
The potential energy of the negative charge increases. The force on the charge will be opposite the direction
to the field, so moving the charge in the direction of the field requires positive work against the field.
Electric potential is defined with respect to position of a unit positive charge. Potential energy of a positive
charge decreases with approach to negative charge. Hence electric potential decreases as we move closer
to a negative charge.
They are related concepts. We can consider the potential energy that a given charge would experience at a
point in an electric field. The electric potential is the potential energy experienced by a unit positive charge at
a point, so it is a quantity that is determined by the field, independent of the test charge (provided it is small
enough not to distort the field).
The electric potential at each point is the same. Identical test charges placed at either point would require the
same force to hold it in place against the present electric field.
No, higher. Electric field lines go from high to low potential. A negatively charged particle which is free to
move will experience a force opposite the direction of the field, so it will move from lower to higher electric
potential, unless you define electric potential to be greater for any charge moved against the force.
No. A negatively charged particle is attracted to the region of higher potential because that region contains
(more) positive charge unless, of course, you are the only conductor around. But at least you would be
insulated from the ground so that you would not discharge violently.
Answers to Exercises
E1
E2
E3
E4
E5
E6
3.0 x 10+13 electrons
+9 C
+4 C each
32 N
3N
a. 14.4 N
b. see diagram below
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E7
a. 1.8 N
b. see diagram below
E8
E9
E10
E11
E12
E13
E14
E15
E16
9.2 x 10-8 N along a straight line from the proton to the electron.
100 N downward
3.0 x 106 N/C downward
2.67 x 106 N/C east
0.26 N to the left
12.5 J
-24 J
20,000 V
a. 0.2 J
b. Decreases
Answers to Synthesis Problems
SP1
a.
b.
c.
d.
e.
SP2
a.
4.5 x 106 N
7.2 x 106 N
2.7 x106 N to the left
1.35 x 108 N/C to the left
8.1 x 106 N to the right
b.
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SP3
a.
b.
SP4.
a.
b. Yes, at point A. Charges at opposite ends of a diagonal would exert equal and opposite forces on a unit
test charge placed at the center.
SP5
a.
b.
c.
d.
-0.12 J
Toward the top plate
Toward the top plate
3.33 x 104 N/C
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