EXERCISE
MEXERCISEULTIPLE CHOICE QUESTIONS
Choose the best possible answer;
1. A charge Q is divided into two parts q and Q-q and separated by a distance The force of repulsion between them will be maximum when:
a.q=Q/4 b. q=Q/3
c. q = Q/2 d. q=Q
2. Three objects are brought close to each other, two at a time. When objects A and B are brought together, they attract. When objects B and C are brought together, they repel. From this, we conclude that
a. A objects A and C possess charges of the same sign.
b. objects A and C possess charges of opposite sign.
c. all three of the objects possess charges of the same sign.
d. one of the objects is neutral
3. Object A has a charge of +2uC, and object B has a charge of +6µC. Which statement is true about the electric forces on the objects?
a. FAB=-3FUA c. 3 FAB=-FBA
b. Fab=- Fba d. FAB=3 FDA
4. Some charge is being given to a conductor. Then its potential
a. Is maximum at surface
b. Is maximum at centre
c. Is remain same throughout the conductor
d. Is maximum somewhere between surface and centre
5. The unit of Electric field intensity is:
a. volt/metre
b. newton/coulomb
c. joule/coulomb.metre
d. All
6. A proton is about 1840 time heavier than an electron. When it is accelerated by a potential difference of 1 kV, its kinetic energy will be:
a. 1840 keV b. 1/1840 keV
c. 1 keV d. 920 keV
7. The electric field at a distance of 20 cm from 2 uC charge is
a. 3x10 N b. 3x10 N
c. 4.5x10³N d. 4.5x10 N
8. An electric charge q is placed at the center of a cube of side "a", the electric flux on its one side will be.
a. q/6 Eo b. q/Ea²
d. q/to c. q/4πEo
9. The electric flux through the surface of a sphere due to a charge q placed at its center depends upon
a. the radius of the sphere
b. the quantity of charge outside the sphere
c. the surface area of the sphere
d. the quantity of charge inside the sphere
10. A one microfarad capacitor of a TV is subjected to 4000 V potential difference.
The energy stored in capacitor is.
A. 8J B. 16 J
c. 4×10-³ J d. 2×10-³ J
11. In the figure below, the charge on 3 uF capacitor is.
a. 5 μc b. 10 μC
c. 3 μC d. 6 µC
12. Two parallel metal plates are 8.00 m apart. The electric field be tween the plates is uniform, directed toward the right, and has a magnitude of 4.00 N/C. If an ion of charge +2e is released at rest at the left-hand plate, what is its kinetic energy when it reaches the right-hand plate?
a. 4 eV b. 64 eV
c. 32 eV d. 16 eV
13. The electric potential between two points A and B is AV. The work done W by the field in moving a charge q from A to B is
a. W = -qAV b.W=qAV
c. W = -q/AV d. W = AV/q
CONCEPTUAL QUESTION
Give a short response to the following questions:
1. The electric potential is constant through a given region of space. Is the electric field zero on non-zero in this region?
Ans:- When electric potential is constant throughout a given region of space, it is not possible to say that electric field in that region is zero or non-zero. It may be zero or non-zero depending upon the situation.
Explanation:- Consider the case of a hollow spherical conducting shell on which charges are symmetrically distributed. Inside the shell the potential is zero (con stant) throughout the region. Also we know that electric field intensity is the neg ative of potential gradient, i.e.
Thus we can say that electric field inside a constant potential is zero. Now there exists a case, where electric field is non-zero when potential V is con stant. Consider a uniform electric field produced by an infinite sheet of charge, in which potential is constant on an equipotential line (dotted lines). Let a point charge q moved from initial point i to final point f through a distance Ar, along an equi potential surface as shown in the figure by the dotted line. The electric potential AV between the two points is;
∆V= 0 (equipotential surface)
Now we know that electric field intensity can bewritten as;
∆V=E.∆r E∆rCos∅
0=E∆rCosⁿ∅
Here exist three possibilities, i.e. either E=0, or ∆r=0 or Cos∅ = 0, but we know that E and ∆r are not equal to zero, thus the only possibility left is that Cos∅ = 0, and the angle for Cos∅ is equal to zero is 90°, thus in case of E and ∆r perpendicular to each other, electric field will exist even when electric potential is constant..
2. If a point charge q of mass m is released in a non-uniform electric field with field lines pointing in the same direction, will it make a rectilinear motion?
Ans:- Yes, a point charge q of mass m released in a non-uniform electric field with field lines pointing in the same direction will make a rectilinear motion.
Explanation: Rectilinear motion is the motion of a body in a straight line, i.e. in one dimension. Whereas a non-uniform electric field is a field which vary in magnitude or direction or in both, but here in this case only magnitude is changing because all field lines are pointing in the same direction as shown in the figure.
Now if a point charge q of mass is released in such a non-uniform electric field Force of electric field (F = qE) will act on it and will produce acceleration in the direction of electric field. So charge particle will move in a straight line (rectilinear motion) with accelerated motion.
3. What is the relationship between potential difference and electric potential energy?
Ans. The relationship between the potential difference and electric potential energy is that the potential difference between two points is equal to the difference in potential energy between these two points divided by a unit charge.
Explanation: Whenever a charged particle is moved from low potential to high potential, work has to be done on it. This work is stored in the body in the form of potential energy. It is represented by AU and is measured in joules. Potential difference Delta*V between two points is the change in potential energy triangle U per unit charge q. in moving it from low potential to high potential. It is measured in volts. Mathematically the relation be tween potential energy and potential difference can be expressed as;
High Potential
Low Potential
4. How are units of volts and electron volts related? How do they differ?
Ans. Volt: The term 'volt' represents unit of potential difference and 1 volt is the potential difference when one joule of work is done in moving 1 Coulomb charge between two points against electric field. Electron Volt: Electron-volt (eV) is the unit of energy and 1 eV is the kinetic energy
gained or lost by an electron when it moves through a P.D. of 1 volt. Relation: The energy E in electron-volts (eV) is equal to the voltage V in volts times the electric charge Q in elementary units (e).
E (e^ prime v) =V (v) * Q (e)
Thus 1 eV energy is equivalent to;
1eV = 1V * 1e
1eV=1Vx1.6x10" C 1eV = 1.6 * 10 ^ - 19
** VC = J Difference: Volt and electron-volt (eV) are two different physical quantities. Elec
tric potential is a property associated with the field, while the energy is associated
with the particle you place into that field and it depends on the particle.
5. How can electric potential be high when the electric potential energy is relatively low?
Ans. Electric potential can be high when electric potential energy is relatively low, if the charge is low as well.
Explanation: Since electric potential at a point in electric field is the potential en ergy possessed by a charge at that point divided by the charge.
Mathematically;
v = U/c
Rightarrow V propto 1 mathfrak q
From the above expression, it is clear that V and q are inversely related. Thus by decreasing the value of q, we can increase the value of electric potential high even when electric potential energy is relatively low.
6. Can the potential of a non-uniformly charged sphere be the same as that of
a point charge?
Ans. Yes, at very large distance the potential of non-uniformly charged sphere the same as that of a point charge.
Explanation: The electric potential due to a point charge is given by;
V= kQ dot r
Consider a spherical shell, on which n number of charges is distributed. Suppose the charges on its surface do not distribute themselves uniformly and thus we get a non uniform distribution of charge. Now at a point lying outside the shell, the electric potential can be given by;
V = k * sum i = 1 to n q_{i}/r_{i}
At a very large distance 'r' from the sphere; the shell may be regarded as a point charge Q. So, in that case the potential is given by;
V = (kQ)/r
*** sum i = 1 to n q_{i}/r_{i} = Q/r
Thus at a very large distance from the sphere the potential due to a non-uniform charged sphere is similar to that of the potential due to a point charge.
7.w
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