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 , Match the following column.

$\begin{matrix} Column-I & Column-II P) Magnitude of magnetic field at point P(2R,0) & 1) Zero Q) X-Component of magnetic field at point P(0,0) & 2) \frac{μ_{0} i}{2 π b} (\frac{a^{2}}{R^{2} - a^{2}}) R) Magnitude of magnetic field at point P(0,0) & 3) \frac{μ_{0} i}{2 π (R^{2} - a^{2})} (\frac{a^{2}}{2 R - b} - \frac{R}{2}) S) Magnitude of magnetic field at point P(0,0) & 4) \frac{μ_{0} i b}{2 π (R^{2} - a^{2})} \end{matrix}$

P $\to$ 2, Q $\to$ 1, R $\to$ 3, S $\to$ 1

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P $\to$ 3, Q $\to$ 2, R $\to$ 4, S $\to$ 1

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P $\to$ 3, Q $\to$ 1, R $\to$ 2, S $\to$ 4

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P $\to$ 4, Q $\to$ 4, R $\to$ 3, S $\to$ 1

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Solution

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 .

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Q. 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{matrix} C o l u m n - I & C o l u m n - I I P) M a g n i t u d e o f m a g n e t i c f i e l d a t p o i n t P (2 R, 0) & 1) Z e r o Q) X - c o m p o n e n t o f m a g n e t i c f i e l d a t p o i n t P (0, 0) & 2) \frac{μ_{0} i}{2 π b} (\frac{a^{2}}{R^{2} - a^{2}}) R) M a g n i t u d e o f m a g n e t i c f i e l d a t p o i n t P (0, 0) & 3) \frac{μ_{0} i}{2 π (R^{2} - a^{2})} (\frac{a^{2}}{2 R - b} - \frac{R}{2}) S) M a g n i t u d e o f m a g n e t i c f i e l d a t p o i n t P (b, 0) & 4) \frac{μ_{0} i b}{2 π (R^{2} - a^{2})} \end{matrix}

Q. A solid cylindrical conductor of radius

R_{1}

is kept inside a hollow cylindrical conductor of inner radius

R_{2}

and outer radius

R_{3} (R_{1} < R_{2} < R_{3})

in a co - axial manner, as shown. The solid cylinder carries a current

I_{1}

and the hollow conductor carries current

I_{2}

in the opposite directions. The two conductors are kept insulated from each other and current through each is distributed uniformly over the cross–section. Let r be any radial distance from the axis.

Magnitude of magnetic induction B at points inside the solid conductor, so that

r < R_{1}

, can be expressed as

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$\begin{matrix} 1. Pituitary gland & P. Thyroxine 2. Thyroid & Q. Growth Hormone, ACTH, Prolactin,TSH 3. Pancreas & R. Other endocrine glands 4. Pineal gland and parathyroid & S. Insulin, glucagon \end{matrix}$

Q. Match the following (column 1 with column 2 )

\begin{matrix} Column 1 & Column 2 p. Monkey & 1. Seasonal breeder q. Bamboo & 2. Annual plant r. Sheep & 3. Perennial plant s. Wheat & 4. Continuous breeder \end{matrix}

Q. Match the following from column 1 and column 2.

\begin{matrix} Column 1 & Column 2 P. Crista and macula & 1. Spinal cord Q. Knee-jerk reflex & 2. Cochlea R. Scala media & 3. Photoreceptor cells S. Rods and cons & 4. Vestibular apparatus \end{matrix}

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The correct option is C P → 3, Q → 1, R → 2, S → 4 Magnetic field intensity of whole complete wire and supposed wire in hole is subtracted .

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 .