Consider the following statements related to the Biot-Savart law:
(A) In SI units, the value of \(\mu_0/4\pi\) is taken as \(10^{-7}\ \mathrm{T\,m\,A^{-1}}\).
(B) The magnetic field due to a current element varies inversely as the distance from the element.
(C) The constant \(\mu_0\) is called the permeability of free space.
(D) A current element at the origin points along the +x direction. Its magnetic field at a point on the +y axis is along the +x direction.
Which of the above statements are incorrect? Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (B) and (D) only
By the Biot-Savart law, the field of a current element is \( d\vec{B}=(\mu_0/4\pi)\,I\,d\vec{l}\times\vec{r}/r^{3} \). Its direction is that of \( d\vec{l}\times\vec{r} \).
(A) In SI units, the value of \(\mu_0/4\pi\) is taken as \(10^{-7}\ \mathrm{T\,m\,A^{-1}}\). — True. This is the value used for the constant in SI units. It gives \( \mu_0=4\pi\times10^{-7}\ \mathrm{T\,m\,A^{-1}} \).
(B) The magnetic field due to a current element varies inversely as the distance from the element. — False. Like the Coulomb field of a point charge, the field of a current element follows an inverse square law. It falls off as \( 1/r^{2} \).
(C) The constant \(\mu_0\) is called the permeability of free space. — True. \( \mu_0 \) is the permeability of free space (vacuum).
(D) A current element at the origin points along the +x direction. Its magnetic field at a point on the +y axis is along the +x direction. — False. Here \( d\vec{l}\times\vec{r} \) is along \( \hat{\imath}\times\hat{\jmath}=\hat{k} \). So the field is along +z, perpendicular to both the element and the line joining it to the point.
NCERT (2026-27):
Magnetic Field Due to a Current Element, Biot-Savart Law – “… The proportionality constant in SI units has the exact value,”
\( \displaystyle \frac{\mu_0}{4\pi}=10^{-7}\ \mathrm{T\,m/A} \)\( \qquad [4.7(c)] \)
Magnetic Field Due to a Current Element, Biot-Savart Law – “The Biot-Savart law for the magnetic field has certain similarities, as well as, differences with the Coulomb’s law for the electrostatic field. … (i) Both are long range, since both depend inversely on the square of distance from the source to the point of interest. …”
Magnetic Field Due to a Current Element, Biot-Savart Law – “We call μ0 the permeability of free space (or vacuum).”
Example 4.4 – “The direction of the field is in the +z-direction.”