Read the following passage and answer the questions.
A student studies the magnetic field produced by a steady current. She uses the Biot-Savart law. First she takes a short straight piece of wire, 1 cm long, placed at the origin. It carries a current of 5 A in the +x direction. She marks some points, each 10 cm from this piece. Some of these points lie on the x-, y- and z-axes. One point, Q, lies in the x-y plane, on a line that makes an angle of 30° with the +x-axis. She also moves a point P along the +y-axis to see how the field changes with distance. Next, she bends a long wire into a flat circular loop of radius \(R\) and passes a steady current \(I\) through it. She treats the loop as a large number of small current elements. She then studies the field at the centre of the loop and at points on its axis.
For the 1 cm piece of wire, match List-I (point, 10 cm from the piece) with List-II (direction of the magnetic field at that point).
| List-I | List-II |
|---|---|
| (A) A point on the +y-axis | (I) Along the −y direction |
| (B) A point on the +x-axis | (II) No field (zero) |
| (C) A point on the +z-axis | (III) Along the +z direction |
| (D) A point on the −y-axis | (IV) Along the −z direction |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A)-(III), (B)-(II), (C)-(I), (D)-(IV)
The field of a current element is along \( d\vec l\times\vec r \), where \( \vec r \) points from the element to the point. Here \( d\vec l \) is along \( \hat i \).
(A) A point on the +y-axis — This matches (III) along the +z direction, because \( \hat i\times\hat j=\hat k \).
(B) A point on the +x-axis — This matches (II) no field. The point lies along the element, so \( \theta=0 \) and \( \sin\theta=0 \).
(C) A point on the +z-axis — This matches (I) along the −y direction, because \( \hat i\times\hat k=-\hat j \).
(D) A point on the −y-axis — This matches (IV) along the −z direction, because \( \hat i\times(-\hat j)=-\hat k \).
NCERT (2026-27):
Magnetic Field Due to a Current Element, Biot-Savart Law – “… Its direction… is perpendicular to the plane containing dl and r.”
Example 4.4 – “The direction of the field is in the +z-direction.”
Magnetic Field Due to a Current Element, Biot-Savart Law – “(iv) There is an angle dependence in the Biot-Savart law which is not present in the electrostatic case. … the magnetic field at any point in the direction of dl (the dashed line) is zero.”
Example 4.4 – “We remind you of the following cyclic property of cross-products,”
\( \hat i\times\hat j=\hat k;\quad \hat j\times\hat k=\hat i;\quad \hat k\times\hat i=\hat j \)