00:02
In this problem, two rods are kept perpendicular to each other and each has length 1 .2 meter.
00:11
Now both are equally charged in magnitude but they have opposite signs.
00:16
First rod has positive charge while the second rods has negative charge.
00:22
Now in first part we have to find net electric field at point p which is at 0 .6 meter that is 60 cm away from both the rods all right so to find the electric field at point p first of all let us look at the directions in which direction they will be are directed so because of the this positive charge if we talk about this horizontal rod then because of these these charges positive charges electric field will be directed away from the rod so it will be in the perpendicular direction so electric field due to this positive rod will be in the downward direction and let us say this electric field is e1.
01:09
Now because of this negative, because of this negative rod, the electric field will be directed towards the rod.
01:18
So it will attract the electric field or the electric field will be directed towards the rod and let us say that this electric field is e2.
01:28
Now we can observe here that both the rods have seemed magnitude of charge that is 2 .5 microculum and both the rods are at equal distance from the point p therefore magnitude of e1 and e2 will be equal so what we can say e1 will be equal to e2 because of the symmetry this modulus sign indicates that their magnitude will be actually equal now question is how to find these magnitudes so for that we will recall a formula that is used to calculate electric field for a uniformly distributed rod.
02:09
So let us say this is the rod on which q charge is uniformly distributed over its entire length l.
02:17
All right.
02:18
And we have to find electric field at point p, which is at a distance r from the rod.
02:27
So if we join the end of these rods, then let us say it is going to make an angle of theta 1 and and theta 2 with the rods.
02:37
Now how to find electric field at point p? so electric field at point p is given by the formula kq divided by lr into sine theta 1 plus sine theta 2.
02:57
So what is here k is representing? k is columns constant.
03:03
Q is the charge which is distributed over it length l is the length of the rod, okay? small r is the perpendicular distance of the point from the rod.
03:15
Theta 1 and theta 2 are the angles made by the end point of the rod with the perpendicular to the rod from the point p.
03:23
So by putting these constants we can get the value of electric field at the point b.
03:29
So we will use this relation to calculate either of e1 or e2 because their magnitudes is going to be same.
03:37
So what will be the value of e1? so if we go to calculate e1, first what is the value of k, k is k is kum's constant and its value is 9 into 10 raise to the power 9 newton meter square per coulomb square.
03:54
Okay, so this is coulum's constant k.
03:57
The second thing is q, that is charge and charge is 2 .5 microculum.
04:03
So micro to convert micro into coulum, we have to multiply it by 10 to the power minus 6 so it will be in column's unit now this is kq divided by l what is the length of the rod it is 1 .2 meter okay and the third thing is small r so what is the smaller smaller was the perpendicular distance and perpendicular distance in both the cases 0 .6 meter that is 60 centimeter so we will put its value in si unit so it will be 0 .6 meter okay now we have to put the value of sine theta 1 and sine theta 2 how to get these values so for that we will join the end points of the rod with the point b okay now this will be theta 1 and this will be theta 2 now if we we have drawn a perpendicular so it will divide these rods in two equal hubs so it will be 0 .6 meter and the second half again will be of 0 .6 meter so it is also 0 .6 meter now if we talk about the first triangle here this right angle triangle so in this right angle triangle base is 0 .6 meter and hypotenous is 0 .6 meter it means that it is an isosceles right angle triangle and what is the property of an a socialisleis right angle triangle that its base angles are equal and that is 45 degree so both of these angle are 45 degree it means that this angle is 45 degree now again the same thing will happen with the second right angle triangle so again this angle is going to be 45 degree so it means that in this case theta 1 and theta 2 are 45 degree so this is theta 2 let us say and this is theta 1 so we have to multiply this factor here we need a few more space so okay so we have to multiply with sine theta 1 that is sine 45 degree plus again sine 45 degree okay so we can solve this value so even comes out to be 4 .42 into 10 to the power 4 newton per column...