# Find the Dimensions of Magnetic Permeability μ 0 the Relevant Equation Are F = Q E , F = Q V B , and B = μ 0 I 2 π a ; Where F is Force, Q is Charge, V is Speed, I is Current, and a is Distance. - Physics

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Find the dimensions of magnetic permeability $\mu_0$
The relevant equation are $F = qE, F = qvB, \text{ and }B = \frac{\mu_0 I}{2 \pi a};$

where F is force, q is charge, v is speed, I is current, and a is distance.

#### Solution

Magnetic permeability,
$\mu_0 = \frac{B \times 2\pi r}{I}$
$\text{ Here,} \left[ B \right] = {\left[ {MT}^{- 2} A^{- 1} \right]}\text{ and } \left[ r \right] = {\left[ L \right]}$
$\text{So, dimension of magnetic permeability,} [ \mu_0 ] = \frac{\left[ {MT}^{- 2} A^{- 1} \right] \times \left[ L \right]}{\left[ A \right]} = \left[ {MLT}^{- 2} A^{- 2} \right]$.

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#### APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 1
Chapter 1 Introduction to Physics
Exercise | Q 3.3 | Page 10
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