Verified Solution • 2025–26 Session moderate

QPages 249-253: Q1: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Due to a Current Pages 249-253: Q1 Solution: Using the formula and show that the SI units of the magnetic…

⚠️ Common Exam Traps & Conceptual Pitfalls

When using $\vec F = q\vec v\times\vec B$, replace the charge unit C with its equivalent $A\cdot s$; the seconds cancel with the velocity $m/s$, yielding $[B]=N\,A^{-1}\,m^{-1}$, not $N\,s\,C^{-1}\,m^{-1}$. Forgetting this conversion leads to an extra time factor and an incorrect unit for $\mu_0$ as well.

Using the formula

\vec{F} = q\vec{v} \times \vec{B}

and

B = \frac{\mu_0 i}{2\pi r}

show that the SI units of the magnetic field B and the permeability constant

\mu_0

may be written as

\text{N m A}^{-1}

and

\text{N A}^{-2}

respectively.

Step-by-Step Verified Solution

**Answer:** From

\vec{F} = q\vec{v} \times \vec{B}

, the SI unit of

B

is

\frac{N}{C \cdot m/s} = \frac{N}{A \cdot m} = N m A^{-1}

. From

B = \frac{\mu_0 i}{2\pi r}

, we get

\mu_0 = \frac{2\pi r B}{i}

. Units:

\frac{m \cdot N m A^{-1}}{A} = N A^{-2}

.

All Questions in this Chapter

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