A wire is formed so as to make a circular loop connecting...

A wire is formed so as to make a circular loop connecting two long, straight sections as shown in Figure $\mathrm{P} 20.72 .$ If the radius of the loop is $R=20 \mathrm{cm}$ and the wire carries current $I=2.4 \mathrm{A}$, what are the magnitude and direction of the magnetic field at the center of the loop?

Key Concepts

Magnetic Field due to a Current Loop

This concept refers to the magnetic field generated at the center (or any point) by a loop of wire carrying an electric current. The field is calculated using the fact that all current elements contribute to the net field, and due to symmetry, in the case of a perfect circle, the field at the center can be expressed in a simple analytical form. The expression commonly used is B = (??I)/(2R), where ?? is the permeability of free space, I is the current, and R is the radius of the loop.

Biot-Savart Law

The Biot-Savart Law is a fundamental principle used to calculate the magnetic field produced by a small segment of current-carrying conductor. It essentially states that the differential magnetic field produced by a current element is proportional to the magnitude of the current, the size and orientation of the element, and inversely proportional to the square of the distance from the element to the point of interest. In the case of a circular loop, integrating the contributions of all such elements yields the net magnetic field at the center.

Right-Hand Rule

The right-hand rule is a mnemonic used to determine the direction of the magnetic field relative to the current direction in a conductor. By pointing the thumb of the right hand in the direction of the current and curling the fingers, one can determine the circular direction of the magnetic field lines around the conductor. For a current loop, this rule helps in identifying whether the magnetic field at the center is directed into or out of the plane of the loop.

Transcript

Please give Ace some feedback