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Class 12 Science (PCM)

Physics Part 1

Moving Charges and Magnetism

Moving Charges and Magnetism

Action PlanNotesQuestionsMock-Test
Study Action Plan (Sorted by Difficulty)
Galvanometer Current and Voltage Sensitivity
Accuracy: 0%
Total Attempted0
Total Correct0
Total Incorrect0
Difficulty Level:
High
Magnetic Field and Force Comparison with Electrostatics
Accuracy: 0%
Total Attempted1
Total Correct0
Total Incorrect1
Difficulty Level:
High
Torque on a Current Loop
Accuracy: 14%
Total Attempted7
Total Correct1
Total Incorrect6
Difficulty Level:
High
Cyclotron Frequency and Energy Independence
Accuracy: 25%
Total Attempted4
Total Correct1
Total Incorrect3
Difficulty Level:
High
Conversion of Galvanometer to Ammeter and Voltmeter
Accuracy: 33%
Total Attempted3
Total Correct1
Total Incorrect2
Difficulty Level:
High
Magnetic Dipole Moment of Current Loop
Accuracy: 38%
Total Attempted8
Total Correct3
Total Incorrect5
Difficulty Level:
High
Moving Coil Galvanometer Principle
Accuracy: 38%
Total Attempted8
Total Correct3
Total Incorrect5
Difficulty Level:
High
Magnetic Force on a Current-Carrying Conductor
Accuracy: 50%
Total Attempted8
Total Correct4
Total Incorrect4
Difficulty Level:
Medium
Motion of Charged Particle in Uniform Magnetic Fiel
Accuracy: 50%
Total Attempted8
Total Correct4
Total Incorrect4
Difficulty Level:
Medium
Ampere's Circuital Law
Accuracy: 60%
Total Attempted5
Total Correct3
Total Incorrect2
Difficulty Level:
Medium
Magnetic Field on Axis of Circular Current Loop
Accuracy: 75%
Total Attempted8
Total Correct6
Total Incorrect2
Difficulty Level:
Low
Magnetic Field Sources and Superposition
Accuracy: 75%
Total Attempted4
Total Correct3
Total Incorrect1
Difficulty Level:
Low
Lorentz Force
Accuracy: 78%
Total Attempted9
Total Correct7
Total Incorrect2
Difficulty Level:
Low
Magnetic Field of a Solenoid
Accuracy: 80%
Total Attempted5
Total Correct4
Total Incorrect1
Difficulty Level:
Low
Biot-Savart Law
Accuracy: 100%
Total Attempted2
Total Correct2
Total Incorrect0
Difficulty Level:
Low
Circular Current Loop as Magnetic Dipole
Accuracy: 100%
Total Attempted2
Total Correct2
Total Incorrect0
Difficulty Level:
Low
Dot-Cross Convention and Right-Hand Rules
Accuracy: 100%
Total Attempted2
Total Correct2
Total Incorrect0
Difficulty Level:
Low
Force Between Parallel Currents
Accuracy: 100%
Total Attempted4
Total Correct4
Total Incorrect0
Difficulty Level:
Low
Magnetic Field due to Long Straight Wire
Accuracy: 100%
Total Attempted1
Total Correct1
Total Incorrect0
Difficulty Level:
Low
Magnetic Field Lines in Current Configurations
Accuracy: 100%
Total Attempted5
Total Correct5
Total Incorrect0
Difficulty Level:
Low
Oersted's Experiment and Magnetic Fields
Accuracy: 100%
Total Attempted5
Total Correct5
Total Incorrect0
Difficulty Level:
Low

Learning Objectives

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Learning Objectives

  • Understand the relationship between electricity and magnetism.
  • Explain the concept of magnetic field lines and their properties.
  • Apply Ampere's Circuital Law to calculate magnetic fields.
  • Derive the expression for the magnetic field due to a long straight wire.
  • Analyze the behavior of magnetic fields in solenoids and coils.
  • Calculate the magnetic moment of a current-carrying loop.
  • Describe the operation of a moving coil galvanometer and its conversion to an ammeter or voltmeter.
  • Solve problems involving the Lorentz force and its implications in electromagnetic theory.
  • Evaluate the effects of parallel and anti-parallel currents on magnetic interactions.

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Revision Notes & Summary

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Chapter Notes: Moving Charges and Magnetism

1. Introduction

  • Electricity and Magnetism have been known for over 2000 years.
  • In 1820, Hans Christian Oersted discovered that a current in a wire deflects a magnetic compass needle, indicating a relationship between electricity and magnetism.

2. Physical Quantities

Physical QuantitySymbolNatureDimensionsUnitsRemarks
Permeability of free spaceµ₀Scalar[MLT⁻²A⁻²]Tm A⁻¹4π X 10⁻⁷ Tm A⁻¹
Magnetic FieldBVector[M T⁻²A⁻¹]T (telsa)
Magnetic MomentmVector[L²A]A m² or J/T
Torsion ConstantkScalar[M L²T⁻²]N m rad⁻¹Appears in MCG

3. Key Concepts

3.1 Electrostatic and Magnetic Fields

  • Electrostatic field lines originate at positive charges and terminate at negative charges or fade at infinity.
  • Magnetic field lines always form closed loops.

3.2 Lorentz Force

  • The expression for the Lorentz force is given by:
    F=q(vimesB+E)F = q (v imes B + E)
  • This force is dependent on the velocity of the charged particle.

3.3 Ampere's Circuital Law

  • Ampere's law relates the magnetic field around a closed loop to the current passing through the loop:
    BimesL=µ0IeB imes L = µ₀ I_e
  • Where:
    • L is the length of the loop
    • I_e is the net current enclosed by the closed circuit.

3.4 Magnetic Field from a Long Straight Wire

  • The magnetic field at a distance R from a long straight wire carrying a current I is given by:
    B = rac{µ₀ I}{2πR}

3.5 Magnetic Field Inside a Solenoid

  • The magnetic field B inside a long solenoid carrying a current I is:
    B=µ0nIB = µ₀ n I
  • Where n is the number of turns per unit length.

4. Important Relationships

  • Parallel currents attract, while anti-parallel currents repel.
  • The magnetic moment m of a planar loop carrying a current I with N turns and area A is:
    m=NimesAm = N imes A

5. Exercises

  • Exercise 4.1: Calculate the magnetic field at the center of a circular coil with 100 turns and radius 8.0 cm carrying a current of 0.40 A.
  • Exercise 4.2: Determine the magnetic field at a point 20 cm from a long straight wire carrying a current of 35 A.
  • Exercise 4.3: Find the magnitude and direction of the magnetic field at a point 2.5 m east of a wire carrying a current of 50 A.

6. Points to Ponder

  1. The relationship between electricity and magnetism is fundamental in understanding electromagnetic phenomena.
  2. The behavior of magnetic fields around current-carrying wires can be visualized using compass needles and iron filings.
  3. The principles of electromagnetism have led to significant technological advancements in the 20th century.
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Practice Test – MCQs, True/False

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Multiple Choice Questions

A.

30 degrees

B.

60 degrees

C.

90 degrees

D.

120 degrees
Correct Answer: B

Solution:

Since the deflection angle ϕ\phi is proportional to the current II, doubling the current doubles the deflection angle. Thus, the new angle is 60 degrees.

Chapter Concept:

Moving Coil Galvanometer Principle

A.

10−5 N/m10^{-5} \text{ N/m}

B.

10−6 N/m10^{-6} \text{ N/m}

C.

10−7 N/m10^{-7} \text{ N/m}

D.

10−4 N/m10^{-4} \text{ N/m}
Correct Answer: A

Solution:

Using the formula f=μ0IaIb2πdf = \frac{\mu_0 I_a I_b}{2\pi d}, where μ0=4π×10−7 Tm/A\mu_0 = 4\pi \times 10^{-7} \text{ Tm/A}, Ia=Ib=5 AI_a = I_b = 5 \text{ A}, and d=0.1 md = 0.1 \text{ m}, the force per meter is f=4π×10−7×5×52π×0.1=10−5 N/mf = \frac{4\pi \times 10^{-7} \times 5 \times 5}{2\pi \times 0.1} = 10^{-5} \text{ N/m}.

Chapter Concept:

Force Between Parallel Currents

A.

Dot represents current/field emerging out of the page and cross represents current/field going into the page.

B.

Dot represents current/field going into the page and cross represents current/field emerging out of the page.

C.

Dot and cross represent electric fields only.

D.

Dot and cross have no specific meaning in physics.
Correct Answer: A

Solution:

The dot-cross convention is used to depict the direction of current or magnetic fields, where a dot indicates an emerging direction and a cross indicates an inward direction.

Chapter Concept:

Dot-Cross Convention and Right-Hand Rules

A.

The magnetic field remains the same.

B.

The magnetic field doubles.

C.

The magnetic field halves.

D.

The magnetic field becomes zero.
Correct Answer: C

Solution:

The magnetic field inside a solenoid is B=μ0nIB = \mu_0 n I, where n=NLn = \frac{N}{L}. If the length LL is doubled, the number of turns per unit length nn halves, hence the magnetic field BB halves.

Chapter Concept:

Magnetic Field of a Solenoid

A.

The deflection angle ϕ\phi remains the same.

B.

The deflection angle ϕ\phi is halved.

C.

The deflection angle ϕ\phi is doubled.

D.

The deflection angle ϕ\phi is quadrupled.
Correct Answer: A

Solution:

The deflection angle ϕ\phi is given by ϕ=NABkI\phi = \frac{NAB}{k}I. Doubling NN and halving AA keeps the product NANA constant, so ϕ\phi remains unchanged.

Chapter Concept:

Moving Coil Galvanometer Principle

A.

The radius remains the same.

B.

The radius doubles.

C.

The radius halves.

D.

The radius quadruples.
Correct Answer: B

Solution:

The radius of the path in a cyclotron is given by r=mvqBr = \frac{mv}{qB}. If the velocity vv is doubled, the radius rr also doubles, as rr is directly proportional to vv.

Chapter Concept:

Cyclotron Frequency and Energy Independence

A.

The deflection angle ϕ\phi is doubled.

B.

The deflection angle ϕ\phi is halved.

C.

The deflection angle ϕ\phi remains the same.

D.

The deflection angle ϕ\phi is quadrupled.
Correct Answer: A

Solution:

The deflection angle ϕ\phi is given by ϕ=NABkI\phi = \frac{NAB}{k}I. Reducing kk to half doubles ϕ\phi for the same current.

Chapter Concept:

Moving Coil Galvanometer Principle

A.

f=μ0IaIb2πdf = \frac{\mu_0 I_a I_b}{2\pi d}

B.

f=μ0IaIbπdf = \frac{\mu_0 I_a I_b}{\pi d}

C.

f=μ0IaIb4πdf = \frac{\mu_0 I_a I_b}{4\pi d}

D.

f=0f = 0
Correct Answer: A

Solution:

The force per unit length between two parallel currents is given by f=μ0IaIb2πdf = \frac{\mu_0 I_a I_b}{2\pi d}, where μ0\mu_0 is the permeability of free space.

Chapter Concept:

Lorentz Force

A.

Concentric circles

B.

Parallel lines

C.

Elliptical loops

D.

Random curves
Correct Answer: A

Solution:

The magnetic field lines around a long straight current-carrying wire form concentric circles centered on the wire.

Chapter Concept:

Magnetic Field Lines in Current Configurations

A.

IABsin⁡(90∘)IAB \sin(90^\circ)

B.

IABcos⁡(90∘)IAB \cos(90^\circ)

C.

IABsin⁡(0∘)IAB \sin(0^\circ)

D.

IABcos⁡(0∘)IAB \cos(0^\circ)
Correct Answer: A

Solution:

The torque on a current loop in a magnetic field is given by τ=IABsin⁡(Θ)\tau = IAB \sin(\Theta), where Θ\Theta is the angle between the magnetic moment and the magnetic field. At 90 degrees, sin⁡(90∘)=1\sin(90^\circ) = 1, so the torque is IABIAB.

Chapter Concept:

Dot-Cross Convention and Right-Hand Rules

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Moving Charges and Magnetism

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True or False

Correct Answer: True

Solution:

The principle of superposition states that the magnetic field of several sources is the vector addition of the magnetic field of each individual source.

Chapter Concept :

Magnetic Field Sources and Superposition

Correct Answer: True

Solution:

According to the magnetic force between two parallel current-carrying wires, parallel currents attract and antiparallel currents repel.

Chapter Concept :

Force Between Parallel Currents

Correct Answer: True

Solution:

The magnetic force on a current-carrying conductor is given by F=Il×BF = I l \times B. If the current and magnetic field are parallel, the angle θ\theta between them is 0∘0^\circ or 180∘180^\circ, making sin⁡θ=0\sin \theta = 0. Therefore, the force is zero.

Chapter Concept :

Magnetic Force on a Current-Carrying Conductor

Correct Answer: True

Solution:

The cyclotron frequency is derived from the angular frequency ω=qBm\omega = \frac{qB}{m} and is given by ν=qB2πm\nu = \frac{qB}{2\pi m}. It does not depend on the speed or radius of the particle, which is a fundamental principle used in cyclotrons.

Chapter Concept :

Cyclotron Frequency and Energy Independence

Correct Answer: True

Solution:

Ampere's Circuital Law is mathematically expressed as ∮B⋅dl=μ0I\oint B \cdot dl = \mu_0 I, where ∮B⋅dl\oint B \cdot dl is the line integral of the magnetic field around the closed loop, μ0\mu_0 is the permeability of free space, and II is the current passing through the loop.

Chapter Concept :

Ampere's Circuital Law

Correct Answer: True

Solution:

The expression for the magnetic field on the axis of a circular current loop is correctly given by B=μ0IR22(x2+R2)3/2B = \frac{\mu_0 I R^2}{2(x^2 + R^2)^{3/2}}. At the center of the loop, where x=0x = 0, this simplifies to B=μ0I2RB = \frac{\mu_0 I}{2R}. For a loop with NN turns, the field is indeed multiplied by NN.

Chapter Concept :

Magnetic Field on Axis of Circular Current Loop

Correct Answer: True

Solution:

According to the principles of magnetism, parallel currents attract each other while antiparallel currents repel. This is derived from the magnetic interactions between current-carrying conductors, as described in the excerpt.

Chapter Concept :

Force Between Parallel Currents

Correct Answer: True

Solution:

Oersted's experiment demonstrated that reversing the current in a wire reverses the direction of the magnetic field, which in turn reverses the orientation of a nearby compass needle.

Chapter Concept :

Oersted's Experiment and Magnetic Fields

Correct Answer: True

Solution:

The dot-cross convention is used to depict the direction of currents or fields in diagrams. A dot represents the tip of an arrow pointing towards the observer, indicating an outward direction, while a cross represents the tail of an arrow moving away, indicating an inward direction.

Chapter Concept :

Dot-Cross Convention and Right-Hand Rules

Correct Answer: True

Solution:

The magnetic force F=q(v×B)F = q(v \times B) is zero when the velocity vv is parallel or antiparallel to the magnetic field BB, as the cross product of parallel vectors is zero.

Chapter Concept :

Lorentz Force

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