What is the magnetic field strength at the center of a circular loop of radius 0.1 m carrying a current of 5 A?
Practice Questions
1 question
Q1
What is the magnetic field strength at the center of a circular loop of radius 0.1 m carrying a current of 5 A?
0.1 T
0.2 T
0.5 T
1 T
The magnetic field at the center of a circular loop is given by B = (μ₀ * I) / (2 * R). Using μ₀ = 4π x 10^-7 Tm/A, B = (4π x 10^-7 * 5) / (2 * 0.1) = 0.1 T.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the magnetic field strength at the center of a circular loop of radius 0.1 m carrying a current of 5 A?
Solution: The magnetic field at the center of a circular loop is given by B = (μ₀ * I) / (2 * R). Using μ₀ = 4π x 10^-7 Tm/A, B = (4π x 10^-7 * 5) / (2 * 0.1) = 0.1 T.
Steps: 8
Step 1: Identify the formula for the magnetic field at the center of a circular loop, which is B = (μ₀ * I) / (2 * R).
Step 2: Note the values needed for the calculation: μ₀ (the permeability of free space) is 4π x 10^-7 Tm/A, I (the current) is 5 A, and R (the radius) is 0.1 m.
Step 3: Substitute the values into the formula: B = (4π x 10^-7 * 5) / (2 * 0.1).
Step 4: Calculate the denominator: 2 * 0.1 = 0.2.
Step 5: Calculate the numerator: 4π x 10^-7 * 5 = 20π x 10^-7.
Step 6: Now divide the numerator by the denominator: B = (20π x 10^-7) / 0.2.
Step 7: Simplify the division: B = 100π x 10^-7 T.
Step 8: Calculate the numerical value: B ≈ 0.1 T (using π ≈ 3.14).
