An electric dipole is placed in a uniform external electric field E → . Show that the torque on the dipole is given by ι → = P → × E → , where P → is the dipole moment.

When an electric dipole is placed in uniform electric field then couple of forces act on dipole which constitute the Turing effect on dipole hence an electric dipole experiences a torque in uniform electric field. This torque is measured by the magnitude either force and perpendicular distance between line of action of force. i . e . , Torque = magnitude of force x Perpendicular distance. T = F × BC = qE × 2 l sinθ In ∆ ABC BC AB = sinθ , BC = 2 lsin θ = ( q · 2 l ) E sinθ = PE sinθ

An electric dipole is placed in a uniform external electric field E → . Show that the torque on the dipole is given by ι → = P → × E → , where P → is the dipole moment.

When an electric dipole is placed in uniform electric field then couple of forces act on dipole which constitute the Turing effect on dipole hence an electric dipole experiences a torque in uniform electric field. This torque is measured by the magnitude either force and perpendicular distance between line of action of force. i . e . , Torque = magnitude of force x Perpendicular distance. T = F × BC = qE × 2 l sinθ In ∆ ABC BC AB = sinθ , BC = 2 lsin θ = ( q · 2 l ) E sinθ = PE sinθ

An electric dipole of dipole moment P → is placed in a uniform electric field E → with its axis inclined to the field. Write an expression for the torque t → experienced by the dipole in vector form. Show diagrammatically how the dipole should be kept in the electric field so that torque acting on it is (i) maximum

We have τ = PE sin θ For τ → τ man m , sin θ = max m = 1 = sin 90 ° ⇒ θ = 90 ° and τ max = PE i . e . , P → and E → Should be perpendicular to each- other means when dipole is arranged as perpendicular to the electric field.

An electric dipole of dipole moment p → is placed in a uniform electric field E → with its axis inclined to the field. Write an expression for the torque τ → experienced by the dipole in vector form. Show diagrammatically how the dipole should be kept in the electric field so that torque acting on it is zero.

The torque acting on the electric dipole: τ = p → × E → = p E sin θ For, τ → τ min m , sin θ = min m = 0 = sin 0 ° ⇒ τ min m = 0 , θ = 0 ° or 180 ° i . e . , P → and E → should be parallel or antiparallel to electric field

What is the force between two small charged spheres carrying charges of 2 × 10 - 7 C and 3 × 10 - 7 C placed 30 cm apart in air?

Given, q 1 = 2 × 10 - 7 C , q 2 = 3 × 10 - 7 C , r = 30 cm = 30 × 10 - 2 m Since both charges have the same nature So, Electrostatic repulsive force = F = 1 4 π ε 0 × q 1 q 2 r 2 = 9 × 10 9 × 2 × 10 - 7 × 3 × 10 - 7 30 × 10 - 2 2 = 9 × 6 × 10 - 5 900 × 10 - 4 N = 6 × 10 - 3 N The charges are of same nature. Hence, force between them will be repulsive.

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IMPORTANT

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An electric dipole is placed in a uniform external electric field $\vec{E}$ . Show that the torque on the dipole is given by $\vec{ι} = \vec{P} \times \vec{E}$ , where $\vec{P}$ is the dipole moment.

Important Questions on Electric Charges and Fields

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12th ICSE

IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 1 - Electric Charges and Fields>QUESTIONS>Q 9

An electric dipole of dipole moment

\vec{P}

is placed in a uniform electric field

\vec{E}

with its axis inclined to the field. Write an expression for the torque

\vec{t}

experienced by the dipole in vector form. Show diagrammatically how the dipole should be kept in the electric field so that torque acting on it is (i) maximum

MEDIUM

12th ICSE

IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 1 - Electric Charges and Fields>QUESTIONS>Q 9

An electric dipole of dipole moment $\vec{p}$ is placed in a uniform electric field $\vec{E}$ with its axis inclined to the field. Write an expression for the torque $\overset{}{\vec{τ}}$ experienced by the dipole in vector form. Show diagrammatically how the dipole should be kept in the electric field so that torque acting on it is zero.

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IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 1 - Electric Charges and Fields>QUESTIONS>Q 1

What is meant by electric dipole and its dipole moment? Obtain an expression for an electric field due to an electric dipole at a point on the perpendicular bisector of the dipole.

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IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 1 - Electric Charges and Fields>QUESTIONS>Q 2

Electric dipole moment is vector or scalar, if it is vector? Show its direction and obtain an expression for an electric field due to an electric dipole at a point on the axis of the electric dipole.

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NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 1 - Electric Charges and Fields>QUESTIONS>Q 3

Define dipole moment of an electric dipole. Show mathematically that the electric field intensity due to a short dipole at a distance r along its axis is twice the intensity at the same distance along the equatorial axis.

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IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 1 - Electric Charges and Fields>QUESTIONS>Q 1

What is the force between two small charged spheres carrying charges of

2 \times 10^{- 7} C

and

3 \times 10^{- 7} C

placed

30

cm apart in air?

MEDIUM

12th ICSE

IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 1 - Electric Charges and Fields>QUESTIONS>Q 2

Calculate the Coulombian force between a proton and an electron separated by

0.8 \times 10^{- 15}

MEDIUM

12th ICSE

IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 1 - Electric Charges and Fields>QUESTIONS>Q 3

Calculate the electrostatic force between

α

-particles separated by

3.2 \times 10^{- 15}

An electric dipole is placed in a uniform external electric field E→. Show that the torque on the dipole is given by ι→=P→×E→, where P→ is the dipole moment.

Important Questions on Electric Charges and Fields

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An electric dipole is placed in a uniform external electric field $\vec{E}$ . Show that the torque on the dipole is given by $\vec{ι} = \vec{P} \times \vec{E}$ , where $\vec{P}$ is the dipole moment.