Question

A very long wire carrying a conventional current of 2.1 amperes is straight except for a circular loop of radius 5.7 cm (see the figure). Calculate the approximate magnitude and the direction of the magnetic field at the center of the loop.

Answer 1

To calculate the magnetic field at the center of the circular loop, we can use Ampere's Law. Using the given values, the magnetic field at the center of the loop is approximately 6.28 × 10^-4 T in the upward direction.

Step-by-step explanation:

To calculate the magnetic field at the center of the circular loop, we can use Ampere's Law. Ampere's Law states that the magnetic field around a closed loop is directly proportional to the current passing through the loop.

Using Ampere's Law for a circular loop, the formula becomes:

B = (μ₀ * I) / (2π * r)

Where B is the magnetic field, μ₀ is the permeability of free space (4π × 10^-7 T*m/A), I is the current, and r is the radius of the loop.

Putting in the given values, the magnetic field at the center of the loop is approximately 6.28 × 10^-4 T in the upward direction.

Answer 2

The magnetic field at the center of a loop in a long wire carrying a current is calculated using Ampère's law. For a loop with a current of 2.1 amperes and radius 5.7 cm, the magnetic field can be found by substituting these values into the formula B = (µ0 * I) / (2 * π * r). The direction of the magnetic field follows the right-hand rule, being perpendicular to the plane of the loop.

Step-by-step explanation:

To calculate the magnetic field at the center of a loop in a long wire carrying a current, we use Ampère's law. The formula to find the magnetic field at the center of a circular loop of wire is B = (µ0 * I) / (2 * π * r), where µ0 is the permeability of free space (4π x 10-7 T·m/A), I is the current, and r is the radius of the loop. With a current (I) of 2.1 amperes and a radius (r) of 5.7 cm (which needs to be converted to meters), we can plug these values into the formula and calculate the magnetic field (B).

First, convert the radius to meters: 5.7 cm = 0.057 m.
Then, substitute the values into the formula: B = (4π x 10-7 T·m/A * 2.1 A) / (2 * π * 0.057 m).
Simplify and compute the value of B, which gives us the magnetic field at the center of the loop.

The direction of the magnetic field is given by the right-hand rule, which states that if you point the thumb of your right hand in the direction of the conventional current, your fingers will curl in the direction of the magnetic field lines. Therefore, the direction of the magnetic field at the center of the loop will be perpendicular to the plane of the loop.