Question

Since the equation for torque on a current-carrying loop is $\mathbf{\pi }\mathbf{=}\mathbf{NIABsin}\mathbf{}\mathbf{\theta }$, the units of $\mathbf{N}\mathbf{‐}\mathbf{m}$must equal units of $\mathbf{A}\mathbf{‐}{\mathbf{m}}^{\mathbf{2}}\mathbf{‐}\mathbf{T}$. Verify this.

Short answer

Yeah our verification affirms that $\mathrm{A}‐{\mathrm{m}}^2‐\mathrm{T}=\mathrm{N}‐\mathrm{m}$

Step-by-step solution

Definition of Torque.

Torque is a measurement of the force required to rotate an object around an axis.

Strategy

To verify the above statement we start with$\mathrm{A}‐{\mathrm{m}}^2‐\mathrm{T}$ and replace the torque with $\frac{\mathrm{N}}{\mathrm{A}‐\mathrm{m}}$.

Verifying units of  is equal to .

Therefore, using the above strategy we get,

$$\begin{gathered} \mathrm{A}‐{\mathrm{m}}^2\mathrm{T}=\mathrm{A}‐{\mathrm{m}}^2‐\frac{\mathrm{N}}{\mathrm{A}‐\mathrm{m}} \\ =\mathrm{N}‐\mathrm{m} \end{gathered}$$

Therefore,$\mathrm{A}‐{\mathrm{m}}^2\mathrm{T}=\mathrm{N}‐\mathrm{m}$