Test: Electric Dipole

QUESTION: 1

Choose the best definition of a dipole.

A.
A pair of equal and like charges located at the origin
B.
A pair of unequal and like charges located at the origin
C.
A pair of equal and unlike charges separated by a small distance
D.
A pair of unequal and unlike charges separated by a small distance

Solution:

Answer: c
Explanation: An electric dipole generally refers to two equal and unlike (opposite signs) charges separated by a small distance. It can be anywhere, not necessarily at origin.

QUESTION: 2

The potential due to a dipole at a point P from it is the

A.
Sum of potentials at the charges
B.
Difference of potentials at the charges
C.
Multiplication of potentials at the charges
D.
Ratio of potentials at the charges

Solution:

Answer: b
Explanation: The total potential at the point P due to the dipole is given by the difference of the potentials of the individual charges.
V = V1 + (-V2), since both the charges are unlike. Thus V = V1 – V2.

QUESTION: 3

Calculate the dipole moment of a dipole with equal charges 2C and -2C separated by a distance of 2cm.

A.
0.02
B.
0.04
C.
0.06
D.
0.08

Solution:

Answer: b
Explanation: The dipole moment of charge 2C and distance 2cm will be,
M = Q x d. Thus, M = 2 x 0.02 = 0.04 C-m.

QUESTION: 4

Find the angle at which the potential due a dipole is measured, when the distance from one charge is 12cm and that due to other is 11cm, separated to each other by a distance of 2cm.

A.
15
B.
30
C.
45
D.
60

Solution:

Answer: d
Explanation: Here, the two charges are separated by d = 2cm.
The distance from one charge (say Q1) will be R1 = 11cm. The distance from another charge (say Q2) will be R2 = 12cm. If R1 and R2 is assumed to be parallel, then R2 – R1 = d cos θ. We get 1 = 2cos θ and cos θ = 0.5. Then θ =
cos^-1(0.5) = 60.

QUESTION: 5

Find the potential due the dipole when the angle subtended by the two charges at the point P is perpendicular.

A.
0
B.
Unity
C.
∞
D.
-∞

Solution:

Answer: a
Explanation: The potential due the dipole is given by, V = m cos θ/(4πεr²). When the angle becomes perpendicular (θ = 90). The potential becomes zero since cos 90 will become zero.

QUESTION: 6

For two charges 3C and -3C separated by 1cm and are located at distances 5cm and 7cm respectively from the point P, then the distance between their midpoint and the point P will be

A.
5.91
B.
12.6
C.
2
D.
9

Solution:

Answer: a
Explanation: For a distant point P, the R1 and R2 will approximately be equal.
R1 = R2 = r, where r is the distance between P and the midpoint of the two charges. Thus they are in geometric progression, R1R2=r²
Now, r2 = 5 x 7 = 35. We get r = 5.91cm.

QUESTION: 7

Calculate the distance between two charges of 4C forming a dipole, with a dipole moment of 6 units.

A.
1
B.
1.5
C.
2
D.
2.5

Solution:

Answer: b
Explanation: The dipole moment is given by, M = Q x d. To get d, we rearrange the formula d = M/Q = 6/4 = 1.5units.

QUESTION: 8

The potential due to the dipole on the midpoint of the two charges will be

A.
0
B.
Unity
C.
∞
D.
-∞

Solution:

Answer: c
Explanation: The potential due a dipole at a point P will be V = m cos θ/(4πεr²).
Now it is given that potential on the midpoint, which means P is on midpoint, then the distance from midpoint and P will be zero. When r = 0 is put in the above equation, we get V = ∞. This shows that the potential of a dipole at its midpoint will be maximum/infinity.

QUESTION: 9

Dipoles in any electric field undergo

A.
Magnetism
B.
Electromagnetism
C.
Magnetisation
D.
Polarisation

Solution:

Answer: d
Explanation: Dipoles in any pure electric field will undergo polarisation. It is the process of alignment of dipole moments in accordance with the electric field applied.

QUESTION: 10

Dipole moments are used to calculate the

A.
Electric field intensity
B.
Polarisation patterns
C.
Strength of the dipole in the field
D.
Susceptibility

Solution:

Answer: b
Explanation: Dipole moment implicates the strength of the dipole in the electric field. They are then used to compute the polarisation patterns based on the applied field. Once the polarisation is determined we can find its susceptibility. Though all options seem to be correct, the apt answer is to calculate polarisation, provided applied field is known.