What is the magnetic field strength at the center of a circular loop of radius 0.1 m carrying a current of 3 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 3 A?
0.03 T
0.1 T
0.15 T
0.2 T
The magnetic field (B) 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 * 3) / (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 3 A?
Solution: The magnetic field (B) 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 * 3) / (2 * 0.1) = 0.1 T.
Steps: 8
Step 1: Identify the formula for the magnetic field (B) at the center of a circular loop. The formula is B = (μ₀ * I) / (2 * R).
Step 2: Identify the values needed for the formula. Here, μ₀ (the permeability of free space) is 4π x 10^-7 Tm/A, I (the current) is 3 A, and R (the radius) is 0.1 m.
Step 3: Substitute the values into the formula. B = (4π x 10^-7 * 3) / (2 * 0.1).
Step 4: Calculate the denominator. 2 * 0.1 = 0.2.
Step 5: Calculate the numerator. 4π x 10^-7 * 3 = 12π x 10^-7.
Step 6: Now divide the numerator by the denominator. B = (12π x 10^-7) / 0.2.
Step 7: Simplify the division. B = 60π x 10^-7 T.
Step 8: Calculate the numerical value. Using π ≈ 3.14, B ≈ 60 * 3.14 x 10^-7 = 188.4 x 10^-7 T = 0.1 T.
