Dimensional Analysis

Step 1: Identify the quantity.
Since the question is incomplete, we hypothesize that it’s asking for the dimensional formula of magnetic permeability

%5Cmu_0

, a common quantity in electromagnetism, given the options involve current

A

with negative exponents. Step 2: Derive the dimensions of

%5Cmu_0

.
The force per unit length between two current-carrying wires is:

%5Cfrac%7BF%7D%7B%5Cell%7D%20%3D%20%5Cfrac%7B%5Cmu_0%20I_1%20I_2%7D%7B2%5Cpi%20d%7D

%5Cmu_0%20%3D%20%5Cfrac%7BF%7D%7B%5Cell%7D%20%5Ccdot%20%5Cfrac%7B2%5Cpi%20d%7D%7BI_1%20I_2%7D

- Force per unit length:

%5BF%2F%5Cell%5D%20%3D%20%5BM%20T%5E%7B-2%7D%5D

- Distance

d

%5Bd%5D%20%3D%20%5BL%5D

- Current

I

%5BI%5D%20%3D%20%5BA%5D

%5B%5Cmu_0%5D%20%3D%20%5Cfrac%7B%5BM%20T%5E%7B-2%7D%5D%20%5BL%5D%7D%7B%5BA%5D%5E2%7D%20%3D%20%5BM%20L%20T%5E%7B-2%7D%20A%5E%7B-2%7D%5D

Step 3: Match with the options.
The dimensional formula

%5BM%20L%20T%5E%7B-2%7D%20A%5E%7B-2%7D%5D

matches option (A).

Step-by-Step Solution for Finding the Dimensions of $(%5Cmu%20%5Cepsilon)%5E%7B-1%7D$

To find the dimensions of $(%5Cmu%20%5Cepsilon)%5E%7B-1%7D$ , we first need to understand the dimensions of permittivity ( $%5Cepsilon$ ) and permeability ( $%5Cmu$ ) in a medium.

Step 1: Identify the formulas for permittivity and permeability:

$%5Cepsilon%20%3D%20%5Cfrac%7B1%7D%7B%5Cmu_0%20c%5E2%7D%2C%20%5Cquad%20%5Cmu%20%3D%20%5Cfrac%7B1%7D%7B%5Cepsilon_0%20c%5E2%7D$

Step 2: Determine the dimensions of permittivity:

$%5B%5Cepsilon%5D%20%3D%20%5BM%5E%7B-1%7D%20L%5E%7B-3%7D%20T%5E4%20A%5E2%5D$

Step 3: Determine the dimensions of permeability:

$%5B%5Cmu%5D%20%3D%20%5BM%20L%20T%5E%7B-2%7D%20A%5E%7B-2%7D%5D$

Step 4: Calculate the dimensions of the product $%5Cmu%20%5Cepsilon$ :

$%5B%5Cmu%20%5Cepsilon%5D%20%3D%20%5BM%20L%20T%5E%7B-2%7D%20A%5E%7B-2%7D%5D%20%5Ctimes%20%5BM%5E%7B-1%7D%20L%5E%7B-3%7D%20T%5E4%20A%5E2%5D%20%3D%20%5BM%5E0%20L%5E%7B-2%7D%20T%5E2%20A%5E0%5D$

Step 5: Find the dimensions of $(%5Cmu%20%5Cepsilon)%5E%7B-1%7D$ :

$(%5Cmu%20%5Cepsilon)%5E%7B-1%7D%20%3D%20%5BM%5E0%20L%5E2%20T%5E%7B-2%7D%20A%5E0%5D%20%3D%20%5BL%5E2%20T%5E%7B-2%7D%5D$

Final Answer: The dimensions of $(%5Cmu%20%5Cepsilon)%5E%7B-1%7D$ are:

$%5BL%5E2%20T%5E%7B-2%7D%5D$

About Dimensional Analysis - CBSE-CLASS-XII

Dimensional Analysis is a vital chapter for CBSE-CLASS-XII aspirants. Mastering the concepts covered in this chapter is essential for securing a top rank.

By rigorously practicing the previous year questions associated with this chapter, you can identify high-yield topics, understand the examiner's perspective, and boost your confidence during the actual exam.

Frequently Asked Questions

Why focus on Dimensional Analysis PYQs?

Analyzing PYQs for this specific chapter reveals the most frequently tested concepts and the typical complexity of questions, allowing you to tailor your study plan efficiently.

How to best use this analysis?

Review the topic breakdown to see which sub-topics within Dimensional Analysis carry the most weight. Then, tackle the questions iteratively to solidify your understanding.

High-Yield Trend

Chapter Questions
2 MCQs

Official Solution

Official Solution

Step-by-Step Solution for Finding the Dimensions of $(%5Cmu%20%5Cepsilon)%5E%7B-1%7D$

About Dimensional Analysis - CBSE-CLASS-XII

Frequently Asked Questions

Why focus on Dimensional Analysis PYQs?

How to best use this analysis?

Dimensional Analysis

High-Yield Trend

Chapter Questions 2 MCQs

Official Solution

Official Solution

Step-by-Step Solution for Finding the Dimensions of

About Dimensional Analysis - CBSE-CLASS-XII

Frequently Asked Questions

Why focus on Dimensional Analysis PYQs?

How to best use this analysis?

Chapter Questions
2 MCQs

Step-by-Step Solution for Finding the Dimensions of $(%5Cmu%20%5Cepsilon)%5E%7B-1%7D$