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Chapter 15: Problem 2182

Unit of \(\mu_{0} \mathrm{c}\) is same as that of (A) current (B) resistance (C) electric charge (D) velocity

Short Answer

Expert verified
None of the given options (A, B, C, or D) has the same unit as the expression \(\mu_{0} \mathrm{c}\), which has the unit \(\frac{\text{T} \cdot \text{m}^{2}}{\text{A} \cdot \text{s}}\).

Step by step solution

01

Identify the components of the expression

In the expression \(\mu_{0} \mathrm{c}\), \(\mu_{0}\) is the permeability of free space value and \(\mathrm{c}\) is the speed of light.
02

Determine the units of each component

The permeability of free space, \(\mu_{0}\), is a constant and has a unit of \(\frac{\text{T} \cdot \text{m}}{\text{A}}\), where T is the unit for magnetic field strength (Tesla), m is the unit of length (meter), and A is the unit of electric current (Ampere). The speed of light, \(\mathrm{c}\), is also a constant and has a unit of \(\frac{\text{m}}{\text{s}}\), where m is the unit of length (meter) and s is the unit of time (second).
03

Determine the unit of the expression

Now, to find the unit of the expression \(\mu_{0} \mathrm{c}\), we simply need to multiply the units of each component: \[ \frac{\text{T} \cdot \text{m}}{\text{A}} \times \frac{\text{m}}{\text{s}} = \frac{\text{T} \cdot \text{m}^{2}}{\text{A} \cdot \text{s}} \]
04

Compare the unit of the expression with the given options

Finally, looking at the options, we check which one has the same unit as \(\frac{\text{T} \cdot \text{m}^{2}}{\text{A} \cdot \text{s}}\): (A) Current: unit is Ampere (A) (B) Resistance: unit is Ohm \(\left( \Omega = \frac{\text{V}}{\text{A}} \right)\) (C) Electric charge: unit is Coulomb (C) (D) Velocity: unit is \(\frac{\text{m}}{\text{s}}\) None of the given options has the same unit as the expression \(\mu_{0} \mathrm{c}\), which means that none of the options (A, B, C, or D) is correct.

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