00:01
We are given a triangular distribution of charges as shown okay so let me just draw the diagram of the triangular setup this is the triangular setup.
00:16
Let this charge be q1 okay, and this charge be q2 and this charge be q3 now it should be noted that q3 is a negative charge.
00:28
So let this be just for illustrative purposes be minus q2 okay.
00:33
Now we are also given that this side if these are the points a, b and c then ab is equal to 8 centimeters and ac is equal to 10 centimeters.
00:49
We need to find what is bc.
00:51
So first things first the magnitude of first charge q1 at a is 0 .8 microcoulombs okay that is it is 0 .8 into 10 raised to the power minus 6 coulombs now the point charge at point b q2 has a negative value negative charge, okay, so q2 has a value of minus 0 .6 microcoulombs okay which is 0 .6 0 .6 into 10 raised to the power minus 6 coulombs now at point c the charge q3 is 1 microcoulombs that is 1 into 10 raised to the power minus 6 coulombs and let this be okay, let this distance be denoted by r1 and let this distance be r2.
01:59
We have to find out bc right means r2 so from pythagoras theorem pythagoras theorem okay, i am writing it in short form for the theorem we have the hypotenuse square that is ac square is equal to the sum of square of other sides that is ab square plus bc square so this implies that this is the pythagoras theorem that bc square or r2 square is equal to ac square minus ab square right, so basically our r2 is equal to under root of ac square minus ab square substituting the values for ac and ab we get this is under root of 100 square minus 64 square basically because the ac is 10 10 square is 100 and ab is 8 8 square is 64 solving which we find that ac r2.
03:21
Sorry bc r2 is equal to 6 centimeters 8 r2 is equal to 6 centimeters now we know that coulombs logically states coulombs law basically can be summarized in as electric field e or the force due to electric field e is equal to k q1 q2 upon r square where q1 and q2 are charges and r is the distance between them k is the constant of electricity it is the electric constant.
04:06
It has a value of 9 into 10 raised to the power 9 newton meter square per coulomb square, okay, so for charges q1 and q2 for charges q1 and q3 if we denote this force by f1 then it is equal to k into q1 into q3 upon r what was this the distance between q1 and q3 is r1.
04:48
Okay, so this will be r1 square okay, this will be r1 square.
04:57
So substituting in our values with this is 9 into 10 raised to the power 9 into q1 is 0 .8 micro coulombs into 10 raised to the power minus 6 q3 is 1 micro coulombs into 10 raised to the power minus 6 upon this is in centimeters upon converting 10 centimeters into meters.
05:21
We will have this is 0 .1 meter whole square here we have used because 10 centimeters is equal to 1 meter using the conversion.
05:30
I'm sorry this is equal to 0 .1 meter.
05:34
We have used the conversion scale where 1 centimeter is equal to 1 hundredth of a meter okay, so solving this calculation.
05:46
We find out that the force between okay, let this be f of 1 3 that is the force between charges q1 and q3 then after calculation this force comes out to be 0 .72 newtons after solving this whole calculation now for charges q2 and q3 okay, this is to be kept in mind.
06:12
Let this be our condition 1 for charges for q2 and q3 let the force force due to the electric field between them be denoted by f of 2 3 this will be equal to k into q2 into q3 into r2 square.
06:36
Okay substituting in our values we will have this as 9 into 10 raised to the power 9 into q2 is 0 .6 micro coulomb...