What is the magnetic field due to a circular loop of radius R carrying current I at a point on its axis at a distance x from the center?
Practice Questions
1 question
Q1
What is the magnetic field due to a circular loop of radius R carrying current I at a point on its axis at a distance x from the center?
μ₀I/(2R)
μ₀I/(2(x² + R²)^(3/2))
μ₀I/(4πR)
μ₀I/(x² + R²)
The magnetic field at a point on the axis of a circular loop at a distance x from the center is given by B = μ₀I/(2(x² + R²)^(3/2)).
Questions & Step-by-step Solutions
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Q
Q: What is the magnetic field due to a circular loop of radius R carrying current I at a point on its axis at a distance x from the center?
Solution: The magnetic field at a point on the axis of a circular loop at a distance x from the center is given by B = μ₀I/(2(x² + R²)^(3/2)).
Steps: 7
Step 1: Understand that we have a circular loop with a radius R and it carries a current I.
Step 2: Identify the point where we want to find the magnetic field. This point is on the axis of the loop and is at a distance x from the center of the loop.
Step 3: Recall the formula for the magnetic field B at a point on the axis of a circular loop: B = μ₀I/(2(x² + R²)^(3/2)).
Step 4: In the formula, μ₀ is the permeability of free space, which is a constant value.
Step 5: The term (x² + R²) represents the distance from the point on the axis to the loop, taking into account both the distance x and the radius R.
Step 6: The expression (x² + R²)^(3/2) means you first add x² and R², then raise the result to the power of 3/2.
Step 7: Finally, plug in the values of μ₀, I, R, and x into the formula to calculate the magnetic field B.
