00:01
In this problem, a circular loop of diameter 10 cm is kept inside a magnetic field.
00:11
So here, diameter d is given which is 10 centimeter.
00:23
So in terms of meter we will divide it by 100, so it will be 0 .1 meter.
00:29
So from here, we can calculate area of the circular loop.
00:34
So area that is a will be equals to pi by 4 d squared.
00:43
So it will be equals to pi by 4 multiplied by 0 .1 meter whole square.
00:52
So from here area comes out to be 7 .854 into 10 raise to the power minus 3 meter square.
01:05
So this is the value of area of the loop.
01:10
Now it is given that the perpendicular unit vector to this area is minus 0 .6 icap and minus 0 .8 jcap.
01:22
So unit vector perpendicular to the loop is minus 0 .6 icap minus 0 .8 jcap.
01:33
Now if perpendicular vector is known to us then from here we can write the value of area vector.
01:40
So area vector will be equal to magnitude of the area that we have calculated earlier into normal vector.
01:50
So this will be equals to 7 .854 into 10 raised to the power minus 3 meter square multiplied by minus 0 .6 i cap minus 0 .8 j cap so from here we get the value of area vector which is 7 .854 into 10 raise to the power minus 3 into minus 0 .6 i cap minus 0 .8 j cap meter square so this is the area vector.
02:36
Now magnetic field b vector is also given in the problem which is 0 .3 tesla k cap.
02:47
And the current inside the loop is 0 .2 ampere.
02:52
So i is the current which is 0 .2 ampere.
02:58
Now we have to find what is the magnitude of the torque.
03:02
So first we can calculate the torque vector.
03:06
So torque vector is given by the formula, n, i, a, cross b, where n is the number of turns, i is the current in loop, a vector is area vector, and b vector is magnetic field.
03:51
So we can put the value of n, i, a, and b here.
03:56
To get the value of torque vector.
03:58
So here number of turns is nothing is mentioned so we will assume n is equal to 1.
04:05
Now we have to put the values here in the above equation so torque vector will be equals to 1 into what is the value of current it is it was 0 .2 ampere into area vector so area vector was 0 was 7 .854 into 10 raised the power minus 3 minus 0 .6 i cap minus 0 .8 j cap now cross product with magnetic field vector which was 0 .3 tesla k cap okay so here these are the these terms are these terms are scalar quantities so we can directly multiply these terms.
05:01
So from here torque vector will be equals to 1 .5708 into 10 raise to the power minus 3.
05:13
Now we will multiply cross product with these two...