Using the three point charges of Example 16.3, find the magnitude of the force on q1 due to the

Using the three point charges of Example 16.3, find the...

Key Concepts

Coulomb's Law

Coulomb's Law describes the electrostatic force between two point charges. It states that the magnitude of the force is directly proportional to the product of the absolute values of the two charges and inversely proportional to the square of the distance between them. This law is fundamental in calculating the forces acting on charges due to mutual electrical interactions.

Vector Decomposition

Vector decomposition involves breaking a vector into its components along specified axes, typically the x- and y-axes. This process allows for simpler calculations when dealing with forces in multiple dimensions, as each component can be handled separately before combining them to determine the resultant force.

Superposition Principle

The superposition principle states that the net force on a charge due to multiple other charges is the vector sum of the individual forces exerted by each charge independently. This principle is crucial when analyzing systems with more than two charges, as it simplifies the calculation of the total force by allowing independent assessment and subsequent combination of each force contribution.

Transcript

00:02 Hi, in the given problem, it is clear that there are x -axis and y -axis in the problem.

00:17 The two charge particles, the positive charge particles out of which one has been kept at the origin because it is kept at a position where x is zero and y is also zero.

00:31 So this is q1 another charge particle q3 is kept here and that is also positive and its distance has been given as 1 .2 meter it can be measured with the help of blocks and the third charge particle this is q2 and that is negative q2.

01:04 Its distance is given as 0 .5 meter along the y -axis.

01:13 So in this way it becomes a right angled triangle and we have to find net force acting at this charge q1 which is kept at the origin.

01:26 So actually there are two forces acting at this q1.

01:30 First of all this q3 will be repelling it like this so here this is f at one due to three and this q2 as it is negative so it will attract it towards itself like this so this is f at one due to two now as we have to find the vector sum of these two forces also so we should have an idea about this angle also that's why first of all we find angle theta for which we use tan theta is equal to perpendicular which is this 0 .5 meter divided by base which is 1 .2 meter here which will come out to be 5 by 12 so so this is 0 .42 and theta will be 10 inverse of 0 .42 which is approximately 22 .8 degree.

03:01 Now we will find the magnitude of these forces, f13 and f12.

03:07 But before finding this f1 2, we should have an idea about the distance between q1 and q2 also and that distance will be given by.

03:15 Pythagoras theorem, let it be r, and that is the square root of 1 .2 square plus 0 .5 square means this is 1 .44 plus 0 .25 means it can be written as 1 .69 meter.

03:42 Now we will find the forces first of all f13 the repulsive force given by a coulum slope k into q1 into q3 divided by the distance between them which is 1 .2 meter to the whole square for k this is 9 into 10 tish per 9 into q1 which is 1 .2 microculum or 1 .2 into 10 dish per minus 6 coulum these values are given in the the figure and for q3 this is 0 .20 microculum or 0 .20 into 10 dash 4 minus 6 column divided by the square of 1 .2 which is 1 .44 so this force finally will come out to be 1 .5 into 10 dash per minus 3 newton now f12 the attractive force using same column slope k into q1 into q2 divided by r square which we have found at the last page so this is 9 into 10 dash per 9 into for q1 again 1 .2 into 10 dash per minus 6 coulom into for q2 this is this is 0 .60 microculem or 0 .60 into 10 dash per minus 6 coulum divided by this tense r square which is 1 .69 it will come out to be so, finally, this force will be 3 .8 into 10 tish power minus 3 newton.

05:16 Now, this force f -13 is purely, this f -1 -3 is purely along x -axis...

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