The Dimensional formula for the electric field is _______

A. [ML²T^-3A^-1]

B. [ML²T^-3A^-2] 

C. [MLT^-3A^-1]

D. [M⁰L⁰T⁰A⁰]

Answer: The correct dimensional formula for the electric field is [MLT⁻³A⁻¹].

An electric field is a region around a charged particle or object where a force is exerted on other charges. The electric field is represented by the symbol E, and its SI unit is newtons per coulomb (N/C) or volts per meter (V/m). It is a fundamental concept in electromagnetism and plays a critical role in understanding forces between charges. To understand the dimensional formula for the electric field, let’s break it down step by step:

Complete Answer:

What is the Electric Field?

The electric field at a point is defined as the force (F) experienced by a unit positive charge (q) placed at that point. Mathematically:

E is the electric field.
F is the force.
q is the charge.

Now, the formula for force is given by Newton’s second law:

F = ma

where m is mass and a is acceleration. The dimensional formula for F is [MLT⁻²].

The dimensional formula for charge (q) is derived from the relationship:

q = I ⋅ t

where 𝐼 is current, and 𝑡 is time. The dimensional formula for 𝑞 is [AT].

Substituting these into the electric field formula:

Evaluating the Options

Let’s match this calculation with the options:

Option A: [ML²T⁻³A⁻¹]

Incorrect. The exponent for L is 2, which doesn’t align with the formula derived above.

Option B: [ML²T⁻³A⁻²]

Incorrect. The charge exponent A^-2  is incorrect here.

Option C: [MLT⁻³A⁻¹]

Correct. This matches the derived dimensional formula for the electric field.

Option D: [M⁰L⁰T⁰A⁰]

Incorrect. This represents a dimensionless quantity, which is not applicable to the electric field.

Additional Insights on Electric Field

Here is some more information about the electric field you should know for a clearer concept: 

Types of Electric Fields:

• Uniform Electric Field: Same magnitude and direction everywhere (e.g., between parallel capacitor plates).
• Non-Uniform Electric Field: Varies in magnitude and/or direction (e.g., around a point charge).

Practical Applications: Electric fields are used in capacitors, cathode ray tubes, and even in modern-day devices like touchscreens.

Fun Fact: The concept of an electric field was first introduced by Michael Faraday in the 19th century to describe forces between charges without physical contact.

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