It is desired to measure the magnitude of field between the poles of a powerful loud speaker magnet.
It is desired to measure the magnitude of field between the poles of a powerful loud speaker magnet. A small flat search coil of area 2 cm2 with 25 closely wound turns, is positioned normal to the field direction, and then quickly snatched out of the field region. Equivalently, one can give it a quick 90° turn to bring its plane parallel to the field direction). The total charge flown in the coil (measured by a ballistic galvanometer connected to coil) is 7.5 mC. The combined resistance of the coil and the galvanometer is 0.50 Ω. Estimate the field strength of magnet.
Area of the small flat search coil, A = 2 cm2 = 2 × 10−4 m2
Number of turns on the coil, N = 25
Total charge flowing in the coil, Q = 7.5 mC = 7.5 × 10−3 C
Total resistance of the coil and galvanometer, R = 0.50 Ω
Induced current in the coil,
$I=\frac{\text { Induced emf }(e)}{R}$ ...(i)
Induced emf is given as:
$e=-N \frac{d \phi}{d t}$ ...(ii)
Where,
$d \phi=$ Charge in flux
Combining equations (1) and (2), we get
$I=-\frac{N \frac{d \phi}{d t}}{R}$
$I d t=-\frac{N}{R} d \phi$ ...(iii)
Initial flux through the coil, $\phi_{i}=B A$
Where,
B = Magnetic field strength
Final flux through the coil, $\phi_{f}=0$
Integrating equation (3) on both sides, we have
$\int I d t=\frac{-N}{R} \int_{\phi}^{\phi_{f}} d \phi$
But total charge, $Q=\int I d t$.
$\therefore Q=\frac{-N}{R}\left(\phi_{f}-\phi_{i}\right)=\frac{-N}{R}\left(-\phi_{i}\right)=+\frac{N \phi_{i}}{R}$
$Q=\frac{N B A}{R}$
$\therefore B=\frac{Q R}{N A}$
$=\frac{7.5 \times 10^{-3} \times 0.5}{25 \times 2 \times 10^{-4}}=0.75 \mathrm{~T}$
Hence, the field strength of the magnet is 0.75 T.
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,