Question

The magnetic field produced by a current carrying circular loop is strongest at

• A. the center of the loop
• B. a point outside the loop
• C. the outer surface of the loop
• D. every point inside the loop

Hint:

Imagine the magnetic field lines passing through the loop. The density of these field lines is highest at the center of the loop, indicating the strongest magnetic field.

Answer 1

The Correct Option is A

Step 1: Recall the magnetic field pattern of a current-carrying circular loop.
A current-carrying circular loop produces a magnetic field pattern similar to that of a bar magnet, with magnetic field lines passing through the center of the loop and forming closed loops. Step 2: Consider the contribution of each segment of the loop to the magnetic field.
According to the Biot-Savart law, the magnetic field \( dB \) produced by a small current element \( dl \) is inversely proportional to the square of the distance from the element and directly proportional to the current and the length of the element. Step 3: Analyze the magnetic field strength at different locations. \begin{enumerate} \item The center of the loop: At the center, the magnetic field contributions from all segments of the circular loop are in the same direction (perpendicular to the plane of the loop) and add up constructively. The distance from each segment to the center is the radius of the loop, which is the minimum distance within the loop's vicinity. \item A point outside the loop: As we move away from the loop, the magnetic field strength decreases with distance. The contributions from different segments of the loop also start to cancel out to some extent. \item The outer surface of the loop: The magnetic field at the surface will be due to the current element closest to that point, but the overall field strength due to the entire loop is weaker compared to the center. \item Every point inside the loop: While the magnetic field exists at every point inside the loop, it is not of uniform strength. The field is strongest at the center and weakens as we move away from the center towards the edges of the loop. \end{enumerate} Step 4: Determine the location of the strongest magnetic field.
Based on the Biot-Savart law and the geometry of the circular loop, the magnetic field is strongest at the center of the loop where the contributions from all parts of the loop add up most effectively.