Question

When the current through a circular loop is 7.5 A, the magnetic field at its center is 5.0 x 10⁻⁴T. What is the radius (in m) of the loop?

Answer 1

To determine the radius of a circular loop with a given magnetic field at the center and current passing through, the formula B = μ0I / (2r) is used. Plugging the values I = 7.5 A and B = 5.0 x 10−4 T, the radius of the loop calculates to approximately 0.0942 meters or 9.42 cm.

Step-by-step explanation:

The student's question involves the calculation of the radius of a circular loop based on the known magnetic field at the center of the loop and the current passing through it.

To solve this, we will use the formula for the magnetic field at the center of a current-carrying loop:

B = μ0I / (2r)

Where B is the magnetic field, μ0 is the vacuum permeability (μ0 = 4π x 10−7 T⋅m/A), I is the current, and r is the radius of the loop.

Rearranging the formula to solve for r:

r = μ0I / (2B)

With the given values I = 7.5 A and B = 5.0 x 10−4 T, we calculate the radius as follows:

r = (4π x 10−7 T⋅m/A 7.5 A) / (2 5.0 x 10−4 T)

= 9.42 x 10−2 m

The radius of the loop is therefore approximately 0.0942 meters or 9.42 cm.