NEET Exam  >  NEET Questions  >  A simple pendulum with Bob mass m and conduct... Start Learning for Free
A simple pendulum with Bob mass m and conducting wire length L swings under gravity through an angle 2(theta) .The earth's magnetic field component in the direction perpendicular to swing is B.What is the maximum potential difference induced across pendulum?
Most Upvoted Answer
A simple pendulum with Bob mass m and conducting wire length L swings ...
**Title: Maximum Potential Difference Induced Across a Simple Pendulum**

**Introduction:**
A simple pendulum consists of a mass (bob) attached to a conducting wire of length L, which is free to swing under the influence of gravity. When the pendulum swings through an angle 2θ, a potential difference is induced across it due to the Earth's magnetic field component B. In this explanation, we will explore the maximum potential difference induced across the pendulum and provide a detailed explanation.

**Understanding the Induced Potential Difference:**
- When a conductor moves in a magnetic field, an emf (electromotive force) is induced across it according to Faraday's law of electromagnetic induction.
- In this case, the conducting wire of the pendulum acts as the moving conductor, and the Earth's magnetic field component acts as the magnetic field.
- As the pendulum swings through an angle 2θ, the length of the wire moving perpendicular to the magnetic field changes, resulting in an induced emf.

**Calculating the Maximum Potential Difference:**
- The maximum potential difference induced across the pendulum can be calculated using the formula:
ΔV = B * L * v * sin(θ)
where ΔV is the potential difference, B is the Earth's magnetic field component, L is the length of the conducting wire, v is the velocity of the pendulum, and θ is the angle of swing.

**Deriving the Maximum Potential Difference Formula:**
- When the pendulum reaches its maximum displacement, all the potential energy is converted into kinetic energy.
- At this point, the velocity of the pendulum can be calculated using the conservation of mechanical energy formula:
m * g * L * (1 - cos(θ)) = 0.5 * m * v^2
where m is the mass of the bob, g is the acceleration due to gravity, L is the length of the conducting wire, θ is the angle of swing, and v is the velocity of the pendulum.
- Solving the above equation for v, we get:
v = sqrt(2 * g * L * (1 - cos(θ)))

**Substituting the Velocity in the Potential Difference Formula:**
- Substituting the expression for v in the potential difference formula, we get:
ΔV = B * L * sqrt(2 * g * L * (1 - cos(θ))) * sin(θ)
- Simplifying this equation further, we can express it as:
ΔV = B * L * sqrt(2gL) * sin(θ) * sqrt(1 - cos(θ))

**Simplifying the Induced Potential Difference Formula:**
- Using trigonometric identities, we can simplify the expression further:
sin(θ) * sqrt(1 - cos(θ)) = sin(θ) * sqrt(sin^2(θ)) = sin^2(θ)
Therefore, the potential difference formula becomes:
ΔV = B * L * sqrt(2gL) * sin^2(θ)

**Conclusion:**
The maximum potential difference induced across the simple pendulum with a bob mass m and conducting wire length L swinging through an angle 2θ under the Earth's magnetic field component B can be calculated using the formula ΔV = B * L * sqrt(2gL) * sin^2(θ). This potential difference is a
Community Answer
A simple pendulum with Bob mass m and conducting wire length L swings ...
Attention NEET Students!
To make sure you are not studying endlessly, EduRev has designed NEET study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in NEET.
Explore Courses for NEET exam

Top Courses for NEET

A simple pendulum with Bob mass m and conducting wire length L swings under gravity through an angle 2(theta) .The earth's magnetic field component in the direction perpendicular to swing is B.What is the maximum potential difference induced across pendulum?
Question Description
A simple pendulum with Bob mass m and conducting wire length L swings under gravity through an angle 2(theta) .The earth's magnetic field component in the direction perpendicular to swing is B.What is the maximum potential difference induced across pendulum? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A simple pendulum with Bob mass m and conducting wire length L swings under gravity through an angle 2(theta) .The earth's magnetic field component in the direction perpendicular to swing is B.What is the maximum potential difference induced across pendulum? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A simple pendulum with Bob mass m and conducting wire length L swings under gravity through an angle 2(theta) .The earth's magnetic field component in the direction perpendicular to swing is B.What is the maximum potential difference induced across pendulum?.
Solutions for A simple pendulum with Bob mass m and conducting wire length L swings under gravity through an angle 2(theta) .The earth's magnetic field component in the direction perpendicular to swing is B.What is the maximum potential difference induced across pendulum? in English & in Hindi are available as part of our courses for NEET. Download more important topics, notes, lectures and mock test series for NEET Exam by signing up for free.
Here you can find the meaning of A simple pendulum with Bob mass m and conducting wire length L swings under gravity through an angle 2(theta) .The earth's magnetic field component in the direction perpendicular to swing is B.What is the maximum potential difference induced across pendulum? defined & explained in the simplest way possible. Besides giving the explanation of A simple pendulum with Bob mass m and conducting wire length L swings under gravity through an angle 2(theta) .The earth's magnetic field component in the direction perpendicular to swing is B.What is the maximum potential difference induced across pendulum?, a detailed solution for A simple pendulum with Bob mass m and conducting wire length L swings under gravity through an angle 2(theta) .The earth's magnetic field component in the direction perpendicular to swing is B.What is the maximum potential difference induced across pendulum? has been provided alongside types of A simple pendulum with Bob mass m and conducting wire length L swings under gravity through an angle 2(theta) .The earth's magnetic field component in the direction perpendicular to swing is B.What is the maximum potential difference induced across pendulum? theory, EduRev gives you an ample number of questions to practice A simple pendulum with Bob mass m and conducting wire length L swings under gravity through an angle 2(theta) .The earth's magnetic field component in the direction perpendicular to swing is B.What is the maximum potential difference induced across pendulum? tests, examples and also practice NEET tests.
Explore Courses for NEET exam

Top Courses for NEET

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev