A Dipole in an Electric Field MCQ Quiz in मल्याळम - Objective Question with Answer for A Dipole in an Electric Field - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക
Last updated on Apr 15, 2025
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A Dipole in an Electric Field Question 1:
If we move from surface to center of a charged metal sphere the electric field will be_____.
Answer (Detailed Solution Below)
A Dipole in an Electric Field Question 1 Detailed Solution
The correct answer is zero at each point.
Key Points
- If we move from the surface to the center of a charged metal sphere the electric field will be zero at each point.
- Excess charges placed on a spherical conductor repel and move until they are evenly distributed, as shown in Figure below.
- The excess charge is forced to the surface until the field inside the conductor is zero.
- Outside the conductor, the field is exactly the same as if the conductor were replaced by a point charge at its center equal to the excess charge.
Additional Information
- Properties of a conductor in electrostatic equilibrium:
- The electric field is zero inside a conductor.
- Just outside a conductor, the electric field lines are perpendicular to its surface, ending or beginning on charges on the surface.
- Any excess charge resides entirely on the surface or surfaces of a conductor.
- A conductor allows free charges to move about within it.
- The electrical forces around a conductor will cause free charges to move around inside the conductor until static equilibrium is reached.
- Any excess charge will collect along the surface of a conductor.
- Conductors with sharp corners or points will collect more charge at those points.
- A lightning rod is a conductor with sharply pointed ends that collect excess charge on the building caused by an electrical storm and allow it to dissipate back into the air.
- Electrical storms result when the electrical field of Earth’s surface in certain locations becomes more strongly charged, due to changes in the insulating effect of the air.
- A Faraday cage acts as a shield around an object, preventing electric charge from penetrating inside.
A Dipole in an Electric Field Question 2:
An electric dipole is placed at an angle of 30° with an electric field of intensity 2 × 105 N C-1. It experiences a torque equal to 4 N m. Calculate the magnitude of charge on the dipole, if the dipole length is 2 cm.
Answer (Detailed Solution Below)
A Dipole in an Electric Field Question 2 Detailed Solution
Concept:
Electric Dipole:
- Electric Dipole: A pair of equal and opposite charges separated by a distance. The dipole moment (p) is given by
, where q is the charge and d is the separation distance. - Torque on Dipole: When placed in an electric field (E), the torque (τ) experienced by the dipole is given by
, where θ is the angle between the dipole moment and the electric field. - SI Unit: The SI unit of torque is Newton-meter (N·m), and the SI unit of electric field is Newton per Coulomb (N/C).
- Dimensional Formula: The dimensional formula for torque is [M L² T²], and for electric field is [M L T³ A¹].
- Important Formula:
and .
Calculation:
Given,
Electric field intensity, E = 2 × 10⁵ N/C
Torque, τ = 4 N·m
Angle, θ = 30°
Dipole length, d = 2 cm = 0.02 m
We know, T = q × d × E × sin30
⇒ 4 = q × d × E × sin30
⇒ 4 = q × 0.02 × 2 × 10⁵ × (1/2)
q = 2 × 10-3
q = 2mC
∴ The correct option is 4)
Hence, the magnitude of charge on the dipole is 2 mC.
A Dipole in an Electric Field Question 3:
An electric dipole of dipole moment p̅ is rotated in an electric field of magnitude E from the most stable orientation to most unstable orientation. The work done in the process is:
Answer (Detailed Solution Below)
A Dipole in an Electric Field Question 3 Detailed Solution
Ans.(2)
Sol.
Equation for work done in rotating dipole from angle 'X1' to angle 'X2'
Work done = P * E (cos X1 - cos X2)
Here, cos X1 = cos0 = 1 (stable)
cos X2 = cos 180 = -1 (unstable)
So,
Work done = P * E (1--1)
= 2PE
A Dipole in an Electric Field Question 4:
Two charges of –4 μC and +4 μC are placed at the points A(1, 0, 4)m and B(2, –1, 5) m located in an electric field
Answer (Detailed Solution Below) 2.00
A Dipole in an Electric Field Question 4 Detailed Solution
Calculation:
⇒
⇒
⇒
⇒
=
⇒ α = 2
∴ the value of α is 2.
A Dipole in an Electric Field Question 5:
The electrostatic potential due to an electric dipole at a distance ‘r’ varies as:
Answer (Detailed Solution Below)
A Dipole in an Electric Field Question 5 Detailed Solution
Concept:
& can also checked dimensionally
∴ The electrostatic potential due to an electric dipole at a distance ‘r’ varies as
A Dipole in an Electric Field Question 6:
Work done to rotate an electric dipole by a 90° angle, is :
Answer (Detailed Solution Below)
A Dipole in an Electric Field Question 6 Detailed Solution
The correct answer is option 4) i.e. PE.
CONCEPT:
- Work done in rotating a dipole in an electric field:
- Consider an electric dipole placed in a uniform electric field E as shown.
- The force due to each of the charges is qE and -qE creating a net force. Since they are separated by a distance, a torque is produced.
Torque, τ = Force × perpendicular distance between charges = qE × 2l sinθ
Electric dipole moment is given by: p = q × 2l
⇒ τ = pEsinθ
Therefore τ = p × E (∵ τ, p, and E are vector quantities)
- Work Done to turn an electric dipole from θ1 to θ2 is given by: WD =
⇒ Work Done = pE [cosθ1 - cosθ2]
CALCULATION:
Given that:
To rotate a dipole by 90∘ ⇒ θ1 = 0∘ and θ2 = 90∘
Work Done = pE [cosθ1 - cosθ2] = pE [cos 0∘ - cos 90∘] = pE [1 - 0] = pE
A Dipole in an Electric Field Question 7:
Two electric dipoles of dipole moments
1.2 × 10-30 C-m and ~2.4 × 10-30 C-m
are placed in two different uniform electric fields of strength
5 × 104 NC-1 and ~15 × 104 NC-1
respectively. The ratio of maximum torque experienced by the electric dipoles will be 1/x. The value of x is _______.
Answer (Detailed Solution Below) 6
A Dipole in an Electric Field Question 7 Detailed Solution
Concept:
The torque τ experienced by an electric dipole in a uniform electric field is given by
τ = pESinθ
For maximum torque, the equation simplifies to:
τ = pE....... ( sinθ = sin 90 = 1)
Calculation:
Given
Dipole moment of the first dipole p1 = 1.2 × 10-30 C-m
Dipole moment of the second dipole p2 = 2.4 × 10-30 C-m
Electric field for the first dipole E1 = 5 × 104 NC-1
Electric field for the first dipole E2 = 15 × 104 NC-1
Maximum Torque for Each Dipole
Torque on the first dipole
⇒τ1 = p1E1 = (1.2 × 10-30) × ( 5 × 104 ) = 6 × 10-26 C.m
Torque on the second dipole
⇒τ2 = p2E2 = (2.4 × 10-30) × ( 15 × 104 ) = 36 × 10-26 C.m
Ratio of Torques:
∴ The value of x = 6
A Dipole in an Electric Field Question 8:
An electric dipole of dipole moment 6.0 × 10–6 Cm placed in a uniform electric field of 1.5 × 103 NC–1 in such a way that dipole moment is along electric field. The work done in rotating dipole by 180° in this field will be __________ mJ.
Answer (Detailed Solution Below) 18
A Dipole in an Electric Field Question 8 Detailed Solution
Concept:
Dipole Moment (p ):
The dipole moment is a vector quantity defined as
P= q.d
where
q is the charge and
d is the separation vector between the charges.
Potential Energy (U) of a Dipole in an Electric Field:
The potential energy of a dipole in a uniform electric field
E is given by:
U=− p ⋅ E
The dot product
U =pEcosθ, where
θ is the angle between the dipole moment p and the electric field E.
Work Done in Rotating the Dipole:
The work done in rotating the dipole from an initial angle to a final angle
W = Vf – Vi in the electric field is equal to the change in potential energy:
W=U.
Calculation:
Work done in rotating the dipole = Vf – Vi
Now, Vf = –PE cos (180°)
Vi = –PE cos 0°
Therefore, W = Vf – Vi
= (–PE cos 180°) – (–PE cos0°)
= 2PE = 2 × 6 × 10–6 × 1.5 × 103 = 18 mJ
∴ The correct answer is (18).
A Dipole in an Electric Field Question 9:
In the given figure the electric field tend to rotate the electric dipole:
Answer (Detailed Solution Below)
A Dipole in an Electric Field Question 9 Detailed Solution
CONCEPT:
Electric dipole in a uniform external field:
- We know that when a charge q is placed in electric field E, it experiences a force F, the force is given as,
⇒ F = qE
- So when an electric dipole is placed in the electric field according to the diagram,
- The force on the +q and the -q charge due to the electric field is given as,
⇒ F = qE
- The net force on the electric dipole will be zero.
- The torque on the electric dipole is given as,
⇒ τ = pE.sinθ
Where θ = angle between the dipole and the electric field
- This torque will tend to align the dipole with the electric field.
EXPLANATION:
- When an electric dipole is placed in an external non-uniform electric field then it is shown as,
In the diagram,
⇒ E = electric field intensity
From figure 1 it is clear that the force on the charge -q will be,
⇒ F1 = qE -----(1)
Similarly from figure 1, it is clear that the force on the charge +q will be,
⇒ F2 = qE -----(2)
- The force F1 and F2 will act opposite to each other.
- The force on the charge -q will act opposite to the electric field while the force on the charge +q acts in the direction of the electric field.
- Since both, the forces are not collinear so the torque will act on the dipole which tries to rotate the dipole anticlockwise. Hence, option 2 is correct.
A Dipole in an Electric Field Question 10:
In the given figure the electric field tend to rotate the electric dipole:
Answer (Detailed Solution Below)
A Dipole in an Electric Field Question 10 Detailed Solution
CONCEPT:
Electric dipole in a uniform external field:
- We know that when a charge q is placed in electric field E, it experiences a force F, the force is given as,
⇒ F = qE
- So when an electric dipole is placed in the electric field according to the diagram,
- The force on the +q and the -q charge due to the electric field is given as,
⇒ F = qE
- The net force on the electric dipole will be zero.
- The torque on the electric dipole is given as,
⇒ τ = pE.sinθ
Where θ = angle between the dipole and the electric field
- This torque will tend to align the dipole with the electric field.
EXPLANATION:
- When an electric dipole is placed in an external non-uniform electric field then it is shown as,
In the diagram,
⇒ E = electric field intensity
From figure 1 it is clear that the force on the charge -q will be,
⇒ F1 = qE -----(1)
Similarly from figure 1, it is clear that the force on the charge +q will be,
⇒ F2 = qE -----(2)
- The force F1 and F2 will act opposite to each other.
- The force on the charge -q will act opposite to the electric field while the force on the charge +q acts in the direction of the electric field.
- Since both, the forces are not collinear so the torque will act on the dipole which tries to rotate the dipole anticlockwise. Hence, option 2 is correct.