(a) A loop of wire carries a conventional current of 0.8 A. The radius of the loop is 0.09 m. Ca

step 1 Given in this question is a circular loop which is of radius 12 cm, that is 0 .12 meter. And for

(a) A loop of wire carries a conventional current of 0.8 A....

(a) A loop of wire carries a conventional current of $0.8 \mathrm{A}$. The radius of the loop is $0.09 \mathrm{m}$. Calculate the magnitude of the magnetic field at a distance of $0.32 \mathrm{m}$ from the center of the loop, along the axis of the loop. (b) What would be the magnitude of the magnetic field at the same location if there were 100 loops of wire in a coil instead of one loop?

Key Concepts

Superposition Principle in Coils

When dealing with multiple current loops, such as in a coil, the total magnetic field is obtained by summing the contributions from each individual loop. The superposition principle allows for the simple scaling of the magnetic field by the number of loops when they are closely spaced and oriented in the same direction. This principle is critical in designing devices like electromagnets and solenoids, where multiple turns are used to enhance the overall magnetic field strength.

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 wire. It is essential for deriving the magnetic field created by more complex current distributions, such as a circular loop. This law relates the magnetic field at a point in space to the magnitude, direction, and distance of the current element from that point, making it a cornerstone in magnetostatics.

Magnetic Field of a Current Loop

This concept involves determining the magnetic field produced by a current flowing in a circular loop. A well-known result is that the magnetic field along the axis of the loop can be expressed in terms of the current, the radius of the loop, and the axial distance from the center. The formula, which stems from integrating the contributions of each current element using the Biot–Savart law, highlights the spatial variation of the magnetic field and is fundamental in understanding how currents generate magnetic fields.

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