Match List-I with List-II.
| List-I | List-II |
|---|---|
| (A) Field of a long straight thin wire, at a distance \(r\) outside it | (I) \(B\propto r\) |
| (B) Field inside a long straight thick wire carrying a uniformly spread current, at a distance \(r\) from its axis | (II) \(B\propto 1/r^{2}\) |
| (C) Field inside a long solenoid, at a distance \(r\) from its axis | (III) \(B\propto 1/r\) |
| (D) Field of a small current element, at a distance \(r\) along a line perpendicular to the element | (IV) \(B\) does not depend on \(r\) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A)-(III), (B)-(I), (C)-(IV), (D)-(II)
Each case follows from Ampere’s law or the Biot-Savart law. The result depends on how much current a loop encloses and how the source is spread out.
(A) Field of a long straight thin wire, at a distance \( r \) outside it — This matches (III) \( B\propto1/r \). The Amperian circle encloses the whole current, so \( B=\mu_0I/2\pi r \).
(B) Field inside a long straight thick wire carrying a uniformly spread current, at a distance \( r \) from its axis — This matches (I) \( B\propto r \). The enclosed current grows as \( r^{2} \) while the loop length grows as \( r \), so \( B=\mu_0Ir/2\pi a^{2} \).
(C) Field inside a long solenoid, at a distance \( r \) from its axis — This matches (IV). The field inside is \( \mu_0nI \) everywhere, so it is the same at any distance from the axis.
(D) Field of a small current element, at a distance \( r \) along a line perpendicular to the element — This matches (II) \( B\propto1/r^{2} \). By the Biot-Savart law, \( dB=\mu_0I\,dl\sin\theta/4\pi r^{2} \).
NCERT (2026-27):
Ampere’s Circuital Law – “… The field is directly proportional to the current and inversely proportional to the distance from the (infinitely long) current source.”
Example 4.7 – “Now the current enclosed Ie is not I, but is less than this value. … Using Ampere’s law,”
\( \displaystyle B=\left(\frac{\mu_0 I}{2\pi a^{2}}\right)r \)\( \qquad [4.15(b)] \)
\( \displaystyle B\propto r\ \ (r\lt a) \)
The Solenoid – “… The solenoid is commonly used to obtain a uniform magnetic field.”
Magnetic Field Due to a Current Element, Biot-Savart Law – “(i) Both are long range, since both depend inversely on the square of distance from the source to the point of interest. …”