If the radius of a circular loop carrying current is doubled, what happens to the magnetic field at the center of the loop?
Practice Questions
1 question
Q1
If the radius of a circular loop carrying current is doubled, what happens to the magnetic field at the center of the loop?
It doubles
It halves
It remains the same
It quadruples
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.
Questions & Step-by-step Solutions
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Q
Q: If the radius of a circular loop carrying current is doubled, what happens to the magnetic field at the center of the loop?
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.
Steps: 7
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.
