The force per unit length of wire B, exerted by wire A is given by F=(kl1 I2)/(r) . Where r is t

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The force per unit length of wire B, exerted by wire A is...

The force per unit length of wire $\mathrm{B}$, exerted by wire $\mathrm{A}$ is given by $\mathrm{F}=\frac{\mathrm{kl}_{1} \mathrm{I}_{2}}{\mathrm{r}} .$ Where $\mathrm{r}$ is the separation between the parallel wires carrying currents $\mathrm{I}_{1}$ and $\mathrm{I}_{2} .$ The dimensional formula of $\mathrm{k}$ is (a) $\mathrm{ML}^{2} \mathrm{~T}^{-2} \mathrm{I}^{2}$ (b) $\mathrm{MLT}^{-2} \mathrm{I}^{-2}$ (c) $\mathrm{ML}^{2} \mathrm{TI}^{2}$ (d) $\mathrm{M}^{2} \mathrm{~L}^{2} \mathrm{~T}^{2} \mathrm{I}^{-2}$

The force per unit length of wire $\mathrm{B}$, exerted by wire $\mathrm{A}$ is given by $\mathrm{F}=\frac{\mathrm{kl}_{1} \mathrm{I}_{2}}{\mathrm{r}} .$ Where $\mathrm{r}$ is the separation between the parallel wires carrying currents $\mathrm{I}_{1}$ and $\mathrm{I}_{2} .$ The dimensional formula of $\mathrm{k}$ is
(a) $\mathrm{ML}^{2} \mathrm{~T}^{-2} \mathrm{I}^{2}$
(b) $\mathrm{MLT}^{-2} \mathrm{I}^{-2}$
(c) $\mathrm{ML}^{2} \mathrm{TI}^{2}$
(d) $\mathrm{M}^{2} \mathrm{~L}^{2} \mathrm{~T}^{2} \mathrm{I}^{-2}$

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Key Concepts

Dimensional Analysis

Dimensional analysis is the method of comparing the dimensions on both sides of an equation to ensure that they match. In physics, this technique is used to determine the dimensions of constants or missing quantities by equating the dimensions derived from each term in an equation, ensuring the law of homogeneity holds true.

Force per Unit Length

The concept of force per unit length refers to how force is distributed along a length of an object, such as a wire. Instead of considering the total force, the focus is on the amount of force acting on a unit segment of the object. Its dimensional formula is derived from the force divided by length, which modifies the dimensions compared to the standard force unit.

Fundamental Dimensions in Electromagnetism

In problems involving electromagnetic interactions, current is treated as a fundamental quantity with its own dimensional symbol (I). When constants like the magnetic permeability or other proportionality constants appear in equations, their dimensions are determined by relating the basic dimensions (mass, length, time, current) from the physical law being considered. This ensures that the overall equation remains dimensionally consistent.

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