{"id":501,"date":"2025-01-22T10:47:09","date_gmt":"2025-01-22T05:17:09","guid":{"rendered":"https:\/\/leverageedu.com\/questions-answers\/?p=501"},"modified":"2025-01-23T11:01:47","modified_gmt":"2025-01-23T05:31:47","slug":"the-dimensional-formula-for-the-electric-field-is","status":"publish","type":"post","link":"https:\/\/leverageedu.com\/questions-answers\/the-dimensional-formula-for-the-electric-field-is\/","title":{"rendered":"The Dimensional formula for the electric field is _______"},"content":{"rendered":"\n

A. [ML2<\/sup>T-3<\/sup>A-1<\/sup>]<\/strong><\/p>\n\n\n\n

B. [ML2<\/sup>T-3<\/sup>A-2<\/sup>]\u00a0<\/sup><\/strong><\/p>\n\n\n\n

C. [MLT-3<\/sup>A-1<\/sup>]<\/strong><\/p>\n\n\n\n

D. [M0<\/sup>L0<\/sup>T0<\/sup>A0<\/sup>]<\/strong><\/p>\n\n\n\n

Answer:<\/strong> The correct dimensional formula for the electric field is [MLT\u207b\u00b3A\u207b\u00b9].<\/strong><\/p>\n\n\n\n

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\u2019s break it down step by step:<\/p>\n\n\n\n

Complete Answer:<\/strong><\/p>\n\n\n\n

What is the Electric Field?<\/strong><\/p>\n\n\n\n

The electric field at a point is defined as the force (F<\/em>) experienced by a unit positive charge (q<\/em>) placed at that point. Mathematically:<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

E<\/strong><\/em> is the electric field.
F<\/strong><\/em> is the force.
q<\/strong><\/em> is the charge.<\/p>\n\n\n\n

Now, the formula for force is given by Newton’s second law:<\/p>\n\n\n\n

F = ma<\/em><\/p>\n\n\n\n

where m<\/em> is mass and a<\/em> is acceleration. The dimensional formula for F is [MLT\u207b\u00b2]<\/strong>.<\/p>\n\n\n\n

The dimensional formula for charge (q<\/em>) is derived from the relationship:<\/p>\n\n\n\n

q = I \u22c5 t<\/em><\/p>\n\n\n\n

where \ud835\udc3c is current, and \ud835\udc61 is time. The dimensional formula for \ud835\udc5e is [AT]<\/strong>.<\/p>\n\n\n\n

Substituting these into the electric field formula:<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Evaluating the Options<\/strong><\/p>\n\n\n\n

Let\u2019s match this calculation with the options:<\/p>\n\n\n\n

Option A: [ML\u00b2T\u207b\u00b3A\u207b\u00b9]<\/strong><\/p>\n\n\n\n

Incorrect. The exponent for L<\/em> is 2, which doesn\u2019t align with the formula derived above.<\/p>\n\n\n\n

Option B: [ML\u00b2T\u207b\u00b3A\u207b\u00b2]<\/strong><\/p>\n\n\n\n

Incorrect. The charge exponent A<\/strong>-2<\/sup><\/strong>  is incorrect here.<\/p>\n\n\n\n

Option C: [MLT\u207b\u00b3A\u207b\u00b9]<\/strong><\/p>\n\n\n\n

Correct. This matches the derived dimensional formula for the electric field.<\/p>\n\n\n\n

Option D: [M\u2070L\u2070T\u2070A\u2070]<\/strong><\/p>\n\n\n\n

Incorrect. This represents a dimensionless quantity, which is not applicable to the electric field.<\/p>\n\n\n\n

Additional Insights on Electric Field<\/strong><\/p>\n\n\n\n

Here is some more information about the electric field you should know for a clearer concept: <\/p>\n\n\n\n

Types of Electric Fields:<\/strong><\/p>\n\n\n\n