If the radius of a circular loop carrying current is doubled, what happens to th

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Question: If the radius of a circular loop carrying current is doubled, what happens to the magnetic field at the center of the loop?

Options:

Correct Answer: It halves

Solution:

The magnetic field at the center of a circular loop is given by B = (μ₀I)/(2r). If the radius is doubled, the magnetic field strength is halved.

If the radius of a circular loop carrying current is doubled, what happens to the magnetic field at the center of the loop?

If the radius of a circular loop carrying current is doubled, what happens to the magnetic field at the center of the loop?

Step 1: Understand that a circular loop carries an electric current.
Step 2: Know that the magnetic field (B) at the center of the loop depends on the current (I) and the radius (r) of the loop.
Step 3: The formula for the magnetic field at the center of the loop is B = (μ₀I)/(2r), where μ₀ is a constant.
Step 4: If the radius (r) of the loop is doubled, replace r in the formula with 2r.
Step 5: The new formula becomes B = (μ₀I)/(2(2r)) = (μ₀I)/(4r).
Step 6: Compare the new formula to the original formula. The new magnetic field is half of the original magnetic field.
Step 7: Conclude that if the radius is doubled, the magnetic field at the center of the loop is halved.

Magnetic Field of a Circular Loop – The relationship between the radius of a circular loop and the magnetic field strength at its center, specifically how changes in radius affect the magnetic field.