Three point charges are fixed in place in a right triangle, as shown in the figure. What is the

Three point charges are fixed in place in a right triangle,...

Key Concepts

Point Charges

A point charge is an idealized model of a charged object in which its size is considered to be so small compared to the distance between charges that its spatial extent can be ignored, allowing the use of simplified formulas for calculating forces.

Coulomb's Law

Coulomb's law quantitatively describes the electric force between two point charges, stating that the magnitude of the force is proportional to the product of the charges and inversely proportional to the square of the distance between them, and it acts along the line joining the charges.

Vector Addition

Vector addition is the process of combining forces that have both magnitude and direction; in problems involving multiple charges, the net force on any given charge is determined by summing the individual force vectors component-wise.

Geometric Analysis

Geometric analysis involves using concepts from geometry, such as the properties of triangles, to resolve the directions of forces into components. In configurations like a right triangle, the use of trigonometric relationships is essential for breaking down vectors along perpendicular axes.

Transcript

00:01 Why, in the given problem there is a net charge which is distributed over two small metallic spheres.

00:09 The net charge is q1 plus q2 is equal to 7 .50 into 10 dash per minus 6 cullum.

00:19 Or we can say we can take it as 7 .50 microculum also.

00:26 Then we can find charge q2 in terms of charge q1 means this is 7 .50 minus q1 microculum.

00:38 These two charges are repelling each other with a force of 20 .0 newton and these charged spheres are kept at a distance of 6 .00 cm between them.

00:53 So we have to find the magnitude of these individual charge particles for which we will use kulam's law which says f is equal to k into q1 into q2 by r squared so plugging in unknown values for a force this is 20 .0 newton for k this is 1 upon 4 pi epsilon not which comes out to be 9 into 10 dash per 9 then for q1 as the charges are measured in microculum so in assignates this q1 will be q1 1 into 10 dash per minus 6 coularm.

01:35 Similarly that is q2 which is 7 .50 minus q1 and that should also be converted into coularm that was microculum because divided by the square of distance which is 6 cm or 6 into 10 to minus 2 meter to the whole square.

01:55 So it will come out to be 9 into 10 dash per minus 3 into q1 into 7 .50 minus 2 minus 1 into 7 .50 minus q1 divided by 36 into 10 to minus 4.

02:13 Or rearranging the terms we will get 7 .50 q1 if we expand this bracket minus q1 square is equal to 20 multiplied by 36 divided by 90.

02:34 Because this 10 dash for minus 4 when it will go up it will become 10 ratio plus 4 and 10 rish for minus 3 when it will be multiplied with this it will remain 10 only then 9 into 10 will be 90 so finally it will come out to be 8 so we get a quadratic equation q1 square minus 7 .50 q1 plus 8 is equal to 0 hence to solve this quadratic we use discriminant formula which says says the root of this equation, q1, will be given by minus b, where b is the multiple of this q1, which is minus 7 .50.

03:30 So, this is minus 7 .50 plus minus discriminant, which is b square minus 4 ac...

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