The figure shows a wire with a loop in it. The current through the wire is 5.00 A and the diameter of the loop is 3.40 cm. What is the magnetic field at the center of the loop?
Question
The figure shows a wire with a loop in it. The current through the wire is 5.00 A and the diameter of the loop is 3.40 cm. What is the magnetic field at the center of the loop?
Solution
To solve this problem, we need to use Ampere's Law which states that the magnetic field around a current carrying wire is given by the formula:
B = μ0I/(2π*r)
Where:
- B is the magnetic field
- μ0 is the permeability of free space, which is a constant equal to 4π x 10^-7 T*m/A
- I is the current through the wire
- r is the radius of the loop
Given in the problem, we have:
- I = 5.00 A
- The diameter of the loop is 3.40 cm, so the radius r = diameter/2 = 3.40 cm / 2 = 1.70 cm = 0.017 m (since we need to convert cm to m)
Substituting these values into the formula, we get:
B = (4π x 10^-7 Tm/A * 5.00 A) / (2π*0.017 m)
Solving this gives us the magnetic field B at the center of the loop.
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