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Concepts Of Physics MCQ Edition [Volume 2]

Exam: Concepts Of Physics MCQ Edition [Volume 2]
Subject: Physics
Chapter: Magnetic Field due to a Current

Concepts Of Physics MCQ Edition [Volume 2] · Physics · Magnetic Field due to a Current

Using the formulae F = q v × B and B = (μ_0 i)/(2π r) , determine...

Using the formulae

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

and

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

, determine the SI units of the magnetic field

B

and the permeability constant

\mu_0

respectively.

Options

A $\text{N A}^{-1}\text{ m}$ and $\text{N m A}^{-2}$
B $\text{N A}^{-1}\text{ m}^{-1}$ and $\text{N A}^{-2}$
C $\text{N m A}^{-1}$ and $\text{N A}^{-2}$
D $\text{N A}^{-2}\text{ m}^{-1}$ and $\text{N A}^{-1}$

Correct answer

B. $\text{N A}^{-1}\text{ m}^{-1}$ and $\text{N A}^{-2}$

Step-by-step solution

From the formula

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

, the magnitude of the magnetic field is given by

B = \dfrac{F}{qv\sin\theta}

.

Substituting the SI units, the unit of

B

is

\dfrac{\text{N}}{\text{C} \cdot \text{m s}^{-1}}

.

Since

\text{C s}^{-1} = \text{A}

, the unit of

B

is

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

.

From the formula

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

, the permeability constant is given by

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

.

Substituting the SI units, the unit of

\mu_0

is

\dfrac{\text{m} \cdot \text{N A}^{-1} \textm^{-1}}{\text{A}} = \text{N A}^{-2}

.

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