Question

A very long straight conductor has a circular cross-section of radius R . Inside the conductor there is a cylindrical hole of radius ‘a’ whose axis is parallel to the axis of the conductor and at a distance ‘b’ from it, as shown in the diagram .The conductor with hole carries current i. Let the z-axis be the axis of conductor and the axis of the hole at x = b, Match the following column.

$$\begin{array}{cc}Column-I& Column-II\\ P\left)MagnitudeofmagneticfieldatpointP\right(2R,0)& 1)Zero\\ Q)X-componentofmagneticfieldatpointP(0,0)& 2)\frac{{\mu }_{0}i}{2\pi b}\left(\frac{a^2}{R^2-a^2}\right)\\ R\left)MagnitudeofmagneticfieldatpointP\right(0,0)& 3)\frac{{\mu }_{0}i}{2\pi (R^2-a^2)}(\frac{a^2}{2R-b}-\frac{R}{2})\\ S\left)MagnitudeofmagneticfieldatpointP\right(b,0)& 4)\frac{{\mu }_{0}ib}{2\pi (R^2-a^2)}\end{array}$$

• A. P $\to$ 2,Q $\to$ 1,R $\to$ 3,S $\to$ 1
• B. P $\to$ 3,Q $\to$ 2,R $\to$ 4,S $\to$ 1
• C. P $\to$ 3,Q $\to$ 1,R $\to$ 2,S $\to$ 4
• D. P $\to$ 4,Q $\to$ 4,R $\to$ 3,S $\to$ 1

Answer 1

The correct option is C P $\to$ 3,Q $\to$ 1,R $\to$ 2,S $\to$ 4

Magnetic field intensity of whole complete wire and supposed wire in hole is subtracted .