What are the dimensions of mu0//4pi?...

What are the dimensions of `mu_0//4pi`?

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To find the dimensions of \(\frac{\mu_0}{4\pi}\), we start by understanding the context in which \(\mu_0\) is used. The term \(\mu_0\) is known as the permeability of free space, and it appears in the formula for the magnetic field due to a current-carrying conductor. ### Step-by-Step Solution: 1. **Identify the formula involving \(\mu_0\)**: The magnetic field \(B\) due to an infinite straight conductor carrying current \(I\) is given by: \[ B = \frac{\mu_0}{4\pi} \cdot \frac{I \cdot dl \cdot \sin \theta}{r^2} ...

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The dimensions of mu_(0) are

`[M^(1)L^(-1//2)T^(1//2)]`

`[M^(1)L^(1//2)T^(-1//2)]`

`[L^(-1)T]`

`[M^(1)L^(1)T^(-2)A^(-2)]`

mu_(0) and epsilon_(0) denote the permeability and permittivity of free space, the dimensions of mu_(0) epsilon_(0) are

`[LT^(-1)]`

`[L^(-2)T^(-2)]`

`[M^(-1)L^(-3)T^(-2)]`

`M^(-1)L^(-3)A^(2)]`

What are the unit of (mu_(0))/(4pi)

`NA^(-1) m^(2)`

`NA^(-2)`

`Nm^(2) C^(2)`

unitless