Question

He magnetic field at the center of a 0.600-cm-diameter loop is 2.80 mT .

What is the current in the loop?

A long straight wire carries the same current you found in part a. At what distance from the wire is the magnetic field 2.80 mT?

Answer 1

The current in the loop is 0.014 A and the distance from the wire where the magnetic field is 2.80 mT is 0.025 m (or 25 cm).

Step-by-step explanation:

To find the current in the loop, we can use the formula

B = (mu_0 * I) / (2 * R)

where B is the magnetic field, mu_0 is the permeability of free space, I is the current, and R is the radius of the loop.

Substituting the given values, we have:

2.80 mT = (4 * pi * 10^-7 T*m/A * I) / (2 * (0.006 cm / 2))

Simplifying the equation, we find that the current in the loop is 0.014 A.

To find the distance from the wire where the magnetic field is 2.80 mT, we can use the formula

B = (mu_0 * I) / (2 * pi * d)

where B is the magnetic field, mu_0 is the permeability of free space, I is the current, and d is the distance from the wire.

Substituting the given values, we have:

2.80 mT = (4 * pi * 10^-7 T*m/A * I) / (2 * pi * d)

Simplifying the equation, we find that the distance from the wire is 0.025 m (or 25 cm).

Answer 2

The magnetic field at the center of a loop is used to calculate the current within the loop, and then, using Ampère's Law, to find the distance from a long straight wire at which the magnetic field is the same magnitude.

Step-by-step explanation:

Current in a Loop and Magnetic Field around a Wire

The magnetic field at the center of a circular loop can be related to the current in the loop through the formula B = µ0I / (2R) where B is the magnetic field, I is the current, and R is the radius of the loop. To find the current I, we need to know the radius. Given that the diameter of the loop is 0.600 cm, the radius is half of that (0.300 cm or 0.003 m). We can rearrange the formula to solve for I and substitute the given values.

For a long straight wire, the magnetic field at a distance r away from the wire is given by B = µ0I / (2πr), where we now solve for r, given that the magnetic field B and current I are known from the previous calculation.