Two concentric co-planar circular Loops of radii r1 and r2 carry currents of respectively I1 and

step 1 In this problem, b1 is equal to mu not i by 2a1 and the value of b2 is equal to mu not i by 2 a2

Two concentric co-planar circular Loops of radii r1 and r2...

Two concentric co-planar circular Loops of radii $\mathrm{r}_{1}$ and $\mathrm{r}_{2}$ carry currents of respectively $\mathrm{I}_{1}$ and $\mathrm{I}_{2}$ in opposite directions. The magnetic induction at the centre of the Loops is half that due to $\mathrm{I}_{1}$ alone at the centre. If $\mathrm{r}_{2}=2 \mathrm{r}_{1}$ the value of $\left(\mathrm{I}_{2} / \mathrm{I}_{1}\right)$ is (a) 2 (b) $1 / 2$ (c) $1 / 4$ (d) 1

Key Concepts

Biot-Savart Law

This fundamental law in magnetostatics describes how moving charges (currents) produce magnetic fields. It is used to derive expressions for the magnetic field at any point in space due to an element of current, and it is notably applied to current loops to obtain the field at their centers.

Magnetic Field Due to a Circular Current Loop

A circular loop carrying a steady current produces a magnetic field at its center given by the formula B = ??I/(2R), where I is the current and R is the radius of the loop. This expression is directly derived from the Biot-Savart Law, and it allows for straightforward computation of the fields from loops with different radii.

Superposition Principle in Magnetostatics

This principle states that the net magnetic field at a point due to multiple sources is the vector sum of the individual fields produced by each source independently. When dealing with concentric loops, it is essential to sum the magnetic fields produced by each loop considering both their magnitudes and directions.

Direction of Magnetic Fields from Currents

The direction of the magnetic field produced by a current loop is determined by the right-hand rule. When multiple loops carry currents in opposite directions, the resulting magnetic fields at a common point can partially cancel each other. This concept is key to solving problems that involve net fields from opposing currents.

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