A circular loop of radius \(R\) carries a steady current \(I\). Consider the following statements:
(A) The magnetic field at the centre of the loop is \(\mu_0I/2R\).
(B) At a point on the axis of the loop, the magnetic field is perpendicular to the axis.
(C) At a large distance \(x\) on the axis \((x\gg R)\), the magnetic field varies as \(1/x^{2}\).
(D) If the fingers of the right hand curl along the current, the thumb gives the direction of the field.
Which of the above statements are incorrect? Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (B) and (C) only
The field of the loop at a distance \( x \) on its axis is \( B=\mu_0IR^{2}/2(x^{2}+R^{2})^{3/2} \), directed along the axis.
(A) The magnetic field at the centre of the loop is \( \mu_0I/2R \). — True. Putting \( x=0 \) gives \( B_0=\mu_0I/2R \).
(B) At a point on the axis of the loop, the magnetic field is perpendicular to the axis. — False. The parts of the field perpendicular to the axis from opposite elements of the loop add to zero. Only the part along the axis remains.
(C) At a large distance \( x \) on the axis \( (x\gg R) \), the magnetic field varies as \( 1/x^{2} \). — False. For \( x\gg R \), the field becomes \( B=\mu_0IR^{2}/2x^{3} \). It varies as \( 1/x^{3} \).
(D) If the fingers of the right hand curl along the current, the thumb gives the direction of the field. — True. This is the right-hand thumb rule for a circular loop.
NCERT (2026-27):
Magnetic Field on the Axis of a Circular Current Loop – “… Here x = 0, and we obtain,”
\( B_0=\frac{\mu_0 I}{2R} \)
Magnetic Field on the Axis of a Circular Current Loop – “… When the components perpendicular to the x-axis are summed over, they cancel out and we obtain a null result. … Thus, only the x-component survives.”
Circular current loop as a magnetic dipole – “… For x >> R, we may drop the R2 term in the denominator. Thus,”
\( B=\frac{\mu_0 I R^{2}}{2x^{3}} \)
Magnetic Field on the Axis of a Circular Current Loop – “Curl the palm of your right hand around the circular wire with the fingers pointing in the direction of the current. The right-hand thumb gives the direction of the magnetic field.”