For a cylindrical conductor of radius R carrying current I, what is the magnetic

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Question: For a cylindrical conductor of radius R carrying current I, what is the magnetic field at a point outside the conductor?

Options:

Correct Answer: μ₀I/2πR

Solution:

Using Ampere\'s Law, B = μ₀I/2πR for points outside the cylindrical conductor.

For a cylindrical conductor of radius R carrying current I, what is the magnetic field at a point outside the conductor?

For a cylindrical conductor of radius R carrying current I, what is the magnetic field at a point outside the conductor?

Step 1: Understand that we have a cylindrical conductor with a certain radius R that carries a current I.
Step 2: Recognize that we want to find the magnetic field (B) at a point that is outside this cylindrical conductor.
Step 3: Recall Ampere's Law, which relates the magnetic field around a conductor to the current flowing through it.
Step 4: According to Ampere's Law, the formula for the magnetic field (B) at a distance R from the center of a long cylindrical conductor is B = μ₀I / (2πR).
Step 5: Note that in this formula, μ₀ is the permeability of free space, I is the current, and R is the distance from the center of the conductor to the point where we are measuring the magnetic field.
Step 6: Conclude that for points outside the cylindrical conductor, we can use this formula to calculate the magnetic field.

Ampere's Law – Ampere's Law relates the magnetic field around a conductor to the current flowing through it, particularly useful for symmetrical current distributions.
Magnetic Field of a Cylinder – The magnetic field outside a long cylindrical conductor can be determined using Ampere's Law, which simplifies the calculation due to symmetry.