Written problem 1 show all work to receive full credit in...

Name: written problem 1 show all work to receive full credit in the figure four long straight wires are perpendicular to the page and their cross sections form a square of edge length a 20 cm the 12592
Uploaded: 2021-09-05T15:12:03-08:00
Duration: 8 min
Channel: Vishal Gupta
Description: written problem 1 show all work to receive full credit in the figure four long straight wires are perpendicular to the page and their cross sections form a square of edge length a 20 cm the 12592

Written Problem 1 (Show all work to receive full credit.) In the figure, four long straight wires are perpendicular to the page, and their cross sections form a square of edge length $a = 20$ cm. The currents are out of the page in wires 1 and 4 and into the page in wires 2 and 3. Each wire carries current 20 A. (A) What are the direction and size of the magnetic field due to the current of wire 1 at the position of wire 4? (B) What are the direction and size of the net magnetic force per meter of wire length on wire 4, due to currents in wire 1, 2, 3 combined? Be sure to draw the three relevant vectors.

Transcript

00:02 Hi, in the given problem four parallel current carrying conductors of infinite lengths are arranged in the form of the square means the four wires are arranged perpendicular to the plane of paper and these wires are behaving like to be arranged at the vertices of this square.

00:43 Here this is wire one, this is wire two, then wire three, and then wire four.

00:53 All the four wires are kept perpendicular to the plane of paper such that here this is x -axis, this is y -axis, this is a square having a side a where the side a is having a magnitude of 20 centimeter or we can say this is 0 .2 meter all these four wires are carrying same current the current having same magnitude 20 ampere each but the directions the wire 1 and 4 are carrying current coming out of the perpendicularly to the plane of paper and wire 2 and 3 are carrying the same currents but getting into the plane of paper now if we look at these diagonals the length of diagonals as we know in a square the diagonals are given as side root 2 means it will be a root 2 or we can say this is 0 .2 into root 2 meter.

02:12 So if we consider this point o at the center of the square then the distance of center of the square from all these current carrying wires will be given by half of the diagonal means it will come out to be 0 .1 square root of 2 which is 1 .414 meter or it can be given as 0 .14 meter now we will find the magnetic fields at this point o whose directions will be found directions of all the magnetic fields at the center of square are found using right hand thumb rule and using that rule the directions of magnetic field first of all if you look for the direction of magnetic field due to the wire at 4 at means the wire 4 this will be here the magnetic field due to the wire number 4 this is b4 and and then due to the wire at 1 and that will be sorry for this wire 4 the magnetic field direction of magnet field due to wire 4 that will be here using right hand thumb rule this is b4 then due to wire 1 due to wire 1 it will be here then due to wire 2 it will be again here this is b2 magnetic field at the center due to wire at point 2 then finally due to 3 this is here this is b3 so now the magnitudes of all these magnetic fields will be same.

05:02 So b1 is equal to b2 is equal to b3 is equal to b4 and that will be equal to mu not upon 4 pi into 2 i by r...

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