If the radius of a circular loop carrying current is doubled, how does the magne

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Question: If the radius of a circular loop carrying current is doubled, how does the magnetic field at the center change?

Options:

Correct Answer: It halves

Solution:

The magnetic field at the center of a circular loop is inversely proportional to the radius; thus, doubling the radius halves the magnetic field.

If the radius of a circular loop carrying current is doubled, how does the magnetic field at the center change?

If the radius of a circular loop carrying current is doubled, how does the magnetic field at the center change?

Step 1: Understand that a circular loop carries an electric current.
Step 2: Know that the magnetic field at the center of the loop depends on the radius of the loop.
Step 3: Remember that the magnetic field (B) is inversely proportional to the radius (r) of the loop. This means that as the radius increases, the magnetic field decreases.
Step 4: If the radius is doubled (made twice as big), we can say that the new radius is 2r.
Step 5: Since the magnetic field is inversely proportional to the radius, if the radius is doubled, the magnetic field becomes half of what it was before.
Step 6: Conclude that doubling the radius of the loop halves the magnetic field at the center.

Magnetic Field of a Circular Loop – The magnetic field at the center of a circular loop carrying current is given by the formula B = (μ₀ * I) / (2 * R), where B is the magnetic field, μ₀ is the permeability of free space, I is the current, and R is the radius of the loop.
Inverse Proportionality – Understanding that the magnetic field strength is inversely proportional to the radius of the loop, meaning as the radius increases, the magnetic field decreases.