Circular loop of a wire and a long straight wire carrying current IC, IE respectively as shown i

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Circular loop of a wire and a long straight wire carrying...

Circular loop of a wire and a long straight wire carrying current $\mathrm{I}_{\mathrm{C}}, \mathrm{I}_{\mathrm{E}}$ respectively as shown in fig. Assuming that these are placed in the same plane. The mag. field will be zero at the centre of the Loop when separation $\mathrm{H}$ is (a) $\left[\left(\mathrm{I}_{\mathrm{e}} \mathrm{R}\right) /\left(\mathrm{I}_{c} \pi\right)\right]$ (b) $\left[\left(\mathrm{I}_{\mathrm{c}} \mathrm{R}\right) /\left(\mathrm{I}_{\mathrm{e}} \pi\right)\right]$ (c) $\left[\left(\pi \mathrm{I}_{\mathrm{c}}\right) /\left(\mathrm{I}_{\mathrm{e}} \mathrm{R}\right)\right]$ (d) $\left[\left(\mathrm{I}_{\mathrm{e}} \pi\right) /\left(\mathrm{I}_{\mathrm{c}} \mathrm{R}\right)\right]$

Circular loop of a wire and a long straight wire carrying current $\mathrm{I}_{\mathrm{C}}, \mathrm{I}_{\mathrm{E}}$ respectively as shown in fig. Assuming that these are placed in the same plane. The mag. field will be zero at the centre of the Loop when separation $\mathrm{H}$ is
(a) $\left[\left(\mathrm{I}_{\mathrm{e}} \mathrm{R}\right) /\left(\mathrm{I}_{c} \pi\right)\right]$
(b) $\left[\left(\mathrm{I}_{\mathrm{c}} \mathrm{R}\right) /\left(\mathrm{I}_{\mathrm{e}} \pi\right)\right]$
(c) $\left[\left(\pi \mathrm{I}_{\mathrm{c}}\right) /\left(\mathrm{I}_{\mathrm{e}} \mathrm{R}\right)\right]$
(d) $\left[\left(\mathrm{I}_{\mathrm{e}} \pi\right) /\left(\mathrm{I}_{\mathrm{c}} \mathrm{R}\right)\right]$

Key Concepts

Magnetic Field of a Circular Current Loop

This concept describes the magnetic field generated at the center of a circular loop when current flows through it. The field is derived from the Biot–Savart law and is directly proportional to the current and inversely proportional to the radius of the loop. This relation allows for calculating the strength of the field at the center, which is essential when considering its interaction with fields from other sources.

Magnetic Field of a Long Straight Conductor

The magnetic field produced by a straight current-carrying wire is described by Ampère’s law or the Biot–Savart law, where the field decreases with distance from the wire. The magnitude of this field at a given point is inversely proportional to the distance of that point from the wire, which is a key factor in determining where and how it may cancel the field of another current source.

Superposition Principle in Magnetostatics

This principle states that the net magnetic field at any point is the vector sum of the magnetic fields produced by each individual current-carrying conductor. It is crucial in problems involving multiple current sources, as it allows for the calculation of conditions (such as specific geometric separations) where the fields cancel each other out.

Application of the Right-Hand Rule

The right-hand rule is used to determine the direction of the magnetic field around a current-carrying conductor. Knowing the direction of the fields created by both the circular loop and the straight wire is necessary to understand and set up the conditions under which the magnetic fields cancel, leading to a zero net field at a particular point.

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