The earth's magnetic induction at a certain point is 7 ×10^-5 Wbm^-2. This is to be annulled by

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The earth's magnetic induction at a certain point is 7...

The earth's magnetic induction at a certain point is $7 \times 10^{-5} \mathrm{Wbm}^{-2}$. This is to be annulled by the magnetic induction at the centre of a circular conducting loop of radius $15 \mathrm{~cm}$. The required current in the loop is (a) $0.56 \mathrm{~A}$ (b) $5.6 \mathrm{~A}$ (c) $0.28 \mathrm{~A}$ (d) $2.8 \mathrm{~A}$

The earth's magnetic induction at a certain point is $7 \times 10^{-5} \mathrm{Wbm}^{-2}$. This is to be annulled by the magnetic induction at the centre of a circular conducting loop of radius $15 \mathrm{~cm}$. The required current in the loop is
(a) $0.56 \mathrm{~A}$
(b) $5.6 \mathrm{~A}$
(c) $0.28 \mathrm{~A}$
(d) $2.8 \mathrm{~A}$

Key Concepts

Magnetic Field from a Circular Current Loop

This concept involves the calculation of the magnetic field generated at the center of a circular loop of conductor carrying a steady current. It is derived from the Biot–Savart law and results in an expression where the field is directly proportional to the current and inversely proportional to the radius of the loop. This formula is fundamental in understanding how current carrying circuits produce magnetic fields in their vicinity.

Biot–Savart Law

The Biot–Savart law provides the method to calculate the magnetic field produced by a small element of current at a point in space. It is essential in deriving the magnetic field of current configurations, such as a circular loop, by integrating the contributions from all current elements. This law forms the basis for understanding more complicated magnetic field distributions in electromagnetism.

Superposition of Magnetic Fields

This principle states that when multiple magnetic fields are present at a point, the net magnetic field is the vector sum of the individual fields. In problems where an externally applied magnetic field (like that from the Earth) must be cancelled or modified by another field (such as that from a current loop), superposition is used to equate and counterbalance these contributions. This concept is central to many applications in electromagnetic design and analysis.

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