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Chapter 15: Problem 2155

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

Short Answer

Expert verified
The unit of the given expression \(\mu_{0} \mathrm{C}\) is tesla meter (Tm). However, none of the options provided in the question match the unit of the given expression. Therefore, the correct answer is not provided in this list.

Step by step solution

01

Identify the units of the given quantities

The given expression is \(\mu_{0} \mathrm{C}\). We need to find the units of this expression. The units for each constant and quantity are as follows: 1. \(\mu_{0}\) (magnetic permeability constant): \( Tm/A \) (tesla meter per ampere) 2. \(\mathrm{C}\) (coulombs): \(A \cdot s \) (ampere seconds)
02

Multiply the units to find the unit of the expression

Now that we've identified the units of each quantity, we will multiply the units of \(\mu_{0}\) and \(\mathrm{C}\) to find the unit of the given expression: Unit of \(\mu_{0} \mathrm{C}\) = (Unit of \(\mu_{0}\)) × (Unit of \(\mathrm{C}\)) Unit of \(\mu_{0} \mathrm{C}\) = \( (Tm/A) \times (As) \) Unit of \(\mu_{0} \mathrm{C}\) = \( Tm \)
03

Compare with the given options

The unit of the given expression, \(Tm\), is tesla meter. Now we'll compare this unit with the units of the options provided in the question: (A) Current: The unit of current is ampere (A), which doesn't match with tesla meter (Tm). (B) Resistance: The unit of resistance is ohm (Ω), which also doesn't match with tesla meter (Tm). (C) Electric charge: The unit of electric charge is coulomb (C), which is not equal to tesla meter (Tm). (D) Velocity: The unit of velocity is meter per second (m/s), which doesn't match with tesla meter (Tm). Since none of the given options have a unit that matches the unit of the given expression, we can conclude that the correct answer is not provided in this list.

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Most popular questions from this chapter

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A plane electromagnetic wave of frequency \(25 \mathrm{MHz}\) travels in free space along the \(\mathrm{x}\) direction. At a particular point in space and time \(\mathrm{E}^{-}=6.3 \mathrm{j} \wedge \mathrm{Vm}^{-1}\) then \(\mathrm{B}^{-}\) at this point is (A) \(2.1 \times 10^{-8}\) i \(\mathrm{T}\) (B) \(2.1 \times 10^{-8} \mathrm{k} \wedge \mathrm{T}\) (C) \(1.89 \times 10^{9} \mathrm{k} \wedge \mathrm{T}\) (D) \(2.52 \times 10^{-7} \mathrm{k} \wedge \mathrm{T}\)
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