Electricity and Magnetism Experiments

Electricity and magnetism physics ke fundamental branches hain, jo electric charges, currents, magnetic fields, and their interactions ko study karte hain. Experiments in fields help students, researchers, aur engineers ko theory ko practically understand karne, instruments ka use seekhne aur applications develop karne me madad karte hain.

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1. Introduction

Electricity: Flow of electric charge (electrons or ions) through a conductor.

Magnetism: Force exerted by magnets or moving charges on other charges or magnetic materials.

Importance of Experiments:

1. Verify Ohm’s Law and Kirchhoff’s Laws
2. Determine resistance, emf, capacitance, and inductance
3. Study magnetic fields and electromagnetic induction
4. Understand Lorentz force, torque on current-carrying loop, and Hall effect

Key Quantities Measured:

• Current (I)
• Voltage (V)
• Resistance (R)
• Magnetic field (B)
• Capacitance (C)
• Inductance (L)

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2. Measurement of Current and Voltage

2.1 Ammeter and Voltmeter

• Ammeter: Measures current in series
• Voltmeter: Measures potential difference in parallel
• Key Considerations:
  • Low resistance for ammeter
  • High resistance for voltmeter

2.2 Ohm’s Law Experiment

• Law: V=IRV = I RV=IR
• Apparatus: Wire, battery, rheostat, ammeter, voltmeter
• Procedure:
  1. Connect circuit with variable resistor
  2. Measure current I and voltage V for various settings
  3. Plot V-I graph → slope = R
• Errors: Contact resistance, instrument calibration, temperature variation

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3. Determination of Resistance

3.1 Using Wheatstone Bridge

• Principle: Null method to measure unknown resistance
• Bridge Balance Condition:

R1R2=RxR3\frac{R_1}{R_2} = \frac{R_x}{R_3}R2​R1​​=R3​Rx​​

Where RxR_xRx​ = unknown resistance

• Procedure:
  1. Connect known resistances in bridge
  2. Adjust sliding contact for zero galvanometer deflection
  3. Calculate RxR_xRx​
• Applications: Laboratory precision measurements

3.2 Using Meter Bridge

• Based on Wheatstone Bridge principle
• Formula:

Rx=Rl1l2R_x = R \frac{l_1}{l_2}Rx​=Rl2​l1​​

Where l1,l2l_1, l_2l1​,l2​ = lengths on meter scale

• Errors: Parallax, contact resistance, temperature variation

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4. Measurement of EMF and Internal Resistance

• Apparatus: Cell, galvanometer, resistors, voltmeter, ammeter
• Procedure:
  1. Measure terminal voltage V for different load currents I
  2. Plot V-I graph
  3. Slope = –r (internal resistance), intercept = emf E
• Formula:

V=E−IrV = E – I rV=E−Ir

• Applications: Battery testing, power supply design

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5. Capacitor Experiments

5.1 Capacitance Measurement

• Apparatus: Parallel plate capacitor, battery, voltmeter, electrometer
• Formula:

C=QV=ϵ0AdC = \frac{Q}{V} = \epsilon_0 \frac{A}{d}C=VQ​=ϵ0​dA​

• Procedure:
  1. Charge capacitor to voltage V
  2. Measure charge Q using electrometer
  3. Calculate capacitance
• Errors: Leakage, stray capacitance, dielectric non-uniformity

5.2 RC Circuit

• Study charging and discharging of capacitor
• Equation:

V(t)=V0(1−e−t/RC),V(t)=V0e−t/RCV(t) = V_0 \left(1 – e^{-t/RC}\right), \quad V(t) = V_0 e^{-t/RC}V(t)=V0​(1−e−t/RC),V(t)=V0​e−t/RC

• Determine time constant τ = RC
• Applications: Filters, timers, signal processing

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6. Current-Carrying Conductor in Magnetic Field

6.1 Magnetic Force Measurement

• Lorentz Force: F=ILBsin⁡θF = I L B \sin \thetaF=ILBsinθ
• Apparatus: Wire, magnets, current source, balance
• Procedure:
  1. Place wire in uniform magnetic field
  2. Pass current I through wire
  3. Measure force F on wire
  4. Verify linear relation between F and I
• Applications: Electric motors, galvanometers

6.2 Tangent Galvanometer Experiment

• Measures current using magnetic field deflection
• Formula:

I=2BRμ0ntan⁡θI = \frac{2 B R}{\mu_0 n} \tan \thetaI=μ0​n2BR​tanθ

• Procedure: Align coil, pass current, measure angle of needle deflection
• Applications: Determination of weak currents

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7. Electromagnetic Induction Experiments

7.1 Faraday’s Law Verification

• Law: Induced emf ϵ=−dΦdt\epsilon = -\frac{d\Phi}{dt}ϵ=−dtdΦ​
• Apparatus: Coil, magnet, galvanometer
• Procedure:
  1. Move magnet into coil
  2. Observe galvanometer deflection
  3. Vary speed to verify ϵ∝dΦ/dt\epsilon \propto d\Phi/dtϵ∝dΦ/dt
• Applications: Generators, transformers

7.2 Lenz’s Law Demonstration

• Direction of induced current opposes the change in flux
• Observe magnet falling through conducting tube → induced current resists motion

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8. Measurement of Magnetic Field

8.1 Using Deflection Magnetometer

• Formula: B=μ0IN2Rsin⁡θB = \frac{\mu_0 I N}{2R} \sin \thetaB=2Rμ0​IN​sinθ
• Procedure:
  1. Place magnetometer in known field
  2. Measure needle deflection
  3. Determine horizontal component of Earth’s magnetic field or field of coil
• Applications: Magnetic field mapping, compass calibration

8.2 Using Helmholtz Coils

• Generate uniform magnetic field
• Field along axis:

B=8μ0NI125RB = \frac{8 \mu_0 N I}{\sqrt{125} R}B=125​R8μ0​NI​

• Applications: Lab calibration, controlled magnetic experiments

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9. Hall Effect Experiment

• Hall voltage: VH=IBnqdV_H = \frac{IB}{n q d}VH​=nqdIB​
• Measures carrier density and type of charge carriers
• Procedure: Pass current through thin conductor in magnetic field
• Measure transverse voltage
• Applications: Magnetic sensors, semiconductor characterization

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10. Errors and Precautions in Electricity and Magnetism Experiments

1. Parallax error: Misalignment of scale and eye
2. Instrumental error: Calibration of ammeter, voltmeter, galvanometer
3. Temperature effects: Resistance of wire changes with temperature
4. Connection errors: Loose contacts in series/parallel circuits
5. Environmental interference: External magnetic fields

• Minimized by proper alignment, repeated readings, calibration, shielding

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11. Numerical Examples

Example 1: Wheatstone Bridge

• R1 = 100 Ω, R2 = 200 Ω, R3 = 150 Ω, bridge balanced

Rx=R3R2R1=150⋅200100=300 ΩR_x = R_3 \frac{R_2}{R_1} = 150 \cdot \frac{200}{100} = 300 \, \OmegaRx​=R3​R1​R2​​=150⋅100200​=300Ω

Example 2: Lorentz Force

• I = 2 A, L = 0.5 m, B = 0.1 T, θ = 90°

F=ILBsin⁡θ=2⋅0.5⋅0.1⋅1=0.1NF = I L B \sin \theta = 2 \cdot 0.5 \cdot 0.1 \cdot 1 = 0.1 NF=ILBsinθ=2⋅0.5⋅0.1⋅1=0.1N

Example 3: RC Time Constant

• R = 1 kΩ, C = 10 μF

τ=RC=1000⋅10×10−6=0.01s\tau = R C = 1000 \cdot 10 \times 10^{-6} = 0.01 sτ=RC=1000⋅10×10−6=0.01s

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12. Summary Table

Experiment	Quantity Measured	Formula / Relation	Instrument
Ohm’s Law	R	V = IR	Ammeter, Voltmeter
Wheatstone Bridge	R_x	Rx=R3R2/R1R_x = R_3 R_2 / R_1Rx​=R3​R2​/R1​	Meter Bridge
Capacitor Measurement	C	C = Q/V	Electrometer
RC Circuit	τ	τ = RC	Capacitor, resistor
Magnetic Force	F	F = ILB sinθ	Balance, wire
Tangent Galvanometer	I	I = (2BR)/(μ₀n) tanθ	Galvanometer, coil
Faraday’s Induction	ε	ε = -dΦ/dt	Coil, magnet, galvanometer
Hall Effect	V_H	V_H = IB / nq d	Hall probe, power supply
Deflection Magnetometer	B	B = μ₀ I N /2R sinθ	Magnetometer

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13. Applications

1. Electric circuits: Testing resistance, EMF, current
2. Magnetic field mapping: Earth’s magnetic field, lab calibration
3. Electrical machines: Generator, motor experiments
4. Semiconductor characterization: Hall effect, carrier density
5. Power supply and electronics labs: RC circuits, capacitors, time constants
6. Industrial applications: Sensors, measurement systems, electromagnetic devices