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A circular loop of radius r is placed in a uniform magnetic field B. If the magn

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Question: A circular loop of radius r is placed in a uniform magnetic field B. If the magnetic field is perpendicular to the plane of the loop, what is the magnetic flux through the loop?

Options:

  1. 0
  2. πr²B
  3. 2πrB
  4. B/r

Correct Answer: πr²B

Solution:

The magnetic flux Φ through a surface is given by Φ = B * A, where A is the area. For a circular loop, A = πr², so Φ = B * πr².

A circular loop of radius r is placed in a uniform magnetic field B. If the magn

Practice Questions

Q1
A circular loop of radius r is placed in a uniform magnetic field B. If the magnetic field is perpendicular to the plane of the loop, what is the magnetic flux through the loop?
  1. 0
  2. πr²B
  3. 2πrB
  4. B/r

Questions & Step-by-Step Solutions

A circular loop of radius r is placed in a uniform magnetic field B. If the magnetic field is perpendicular to the plane of the loop, what is the magnetic flux through the loop?
  • Step 1: Understand that magnetic flux (Φ) measures how much magnetic field passes through a surface.
  • Step 2: Know the formula for magnetic flux: Φ = B * A, where B is the magnetic field strength and A is the area of the surface.
  • Step 3: Identify that the area (A) of a circular loop is calculated using the formula A = πr², where r is the radius of the loop.
  • Step 4: Substitute the area formula into the magnetic flux formula: Φ = B * (πr²).
  • Step 5: Conclude that the magnetic flux through the loop is given by Φ = B * πr².
  • Magnetic Flux – Magnetic flux is the product of the magnetic field and the area through which it passes, taking into account the angle between the field and the normal to the surface.
  • Area of a Circle – The area of a circular loop is calculated using the formula A = πr², where r is the radius of the circle.
  • Uniform Magnetic Field – A uniform magnetic field has the same strength and direction at all points in the region.
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