What is the magnetic field at a point on the axis of a circular loop of radius R
Practice Questions
Q1
What is the magnetic field at a point on the axis of a circular loop of radius R carrying current I?
μ₀I/(2R)
μ₀I/(4R)
μ₀I/(2R²)
μ₀I/(2√2R)
Questions & Step-by-Step Solutions
What is the magnetic field at a point on the axis of a circular loop of radius R carrying current I?
Step 1: Understand that we have a circular loop with a certain radius R.
Step 2: Know that the loop carries an electric current I.
Step 3: Identify the point where we want to find the magnetic field; this point is along the axis of the loop at a distance z from the center of the loop.
Step 4: Recall the formula for the magnetic field B at that point, which is B = (μ₀I/(2R)) * (1/(1 + (z/R)²)^(3/2)).
Step 5: In the formula, μ₀ is the permeability of free space, a constant value.
Step 6: The term (z/R) represents the ratio of the distance z to the radius R of the loop.
Step 7: The expression (1 + (z/R)²) calculates how the distance affects the magnetic field strength.
Step 8: The entire formula shows how the magnetic field B depends on the current I, the radius R, and the distance z.
