Charges of +2.0, +3.0, and -8.0 μC are placed in air at the vertices of an equilateral triangle

Charges of +2.0, +3.0, and -8.0 μC are placed in air at the...

Key Concepts

Coulomb's Law

A fundamental principle in electrostatics that describes the force between two point charges. The law states that the electrostatic force is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them, expressed mathematically as F = k|q1*q2|/r^2, where k is Coulomb’s constant.

Superposition Principle

A key concept in physics stating that the net effect (such as force) on a charge due to multiple other charges is the vector sum of the individual effects. This principle allows the analysis of complex charge systems by considering and then summing each pairwise interaction independently.

Vector Addition

A method used to combine forces that have both magnitude and direction. When calculating the net force from multiple charges, each individual force must be decomposed into its components and then added together, ensuring that both magnitude and direction are accurately accounted for.

Electrostatic Force

The force of attraction or repulsion between charged objects. This concept is central in understanding how charged particles interact in a medium, such as air, and forms the basis for calculations using Coulomb's law.

Transcript

00:01 In this given problem there is an equilateral, equilateral triangle and the three charged particles are kept at its three vertices.

00:17 We may name this triangle as a, v and c.

00:29 The charge kept at a is minus 8 .0 micropoleum at b this is plus 2 .0 microculum and at c this is plus 3 .0 microculum the side of triangle is given as 10 cm each and we know angle of an equilateral triangle is 60 degree now we have to find net force experienced by this charge minus 8 .0 microculum which is put at a so it is experiencing two forces we have to find net force experienced by it and it is experiencing two forces one of the force of attraction towards plus 2 .0 microculum another force of attraction towards plus three microculem we may name these forces as f at a due to b and f at a due to c now using coularm's law we will find magnitude of these two forces first of all f a b will be given as k into q a into q b by a square where a is the side of this triangle for k this is 9 into 10 dash to par 9 for q a that is we will take magnitude only this is 8 microculum or 8 into 10 dash per minus 6 coulum for b this is 2 into 10 dash per minus 6 coulum divided by 10 centimeter or 10 into 10 as far minus 2 meter having a square of it and finally this force comes out to be 14 .4 newton then f at a due to c a into qa into qc divided by a square again so this is 9 into 10 dash per 9 for qa again this is 8 into 10 dash minus 6 coulame but for qc this is 3 into 10 dash per minus 6 coulum and the distance 10 into 10 dash per minus 2 meter having a square of it and this force here comes out to be 21 .6 newton and angle between them theta that is 60 degree so, using triangle of a tradition, net force experienced by this charge put at a, it will be given by square root of square of f at a due to b, plus square of f at a due to c plus two times of fab into fac into cosine of angle.

04:07 Between them.

04:10 So here it will be f a b that is 14 .4 square plus f ac that is 21 .6 square plus two times of 14 .4 into 21 .6 into cosine of 60 degree and cosine of 60 degree will be 1 by 2 this 1 by 2 will be cancelled by this two...

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