-? Repeat Problem 28.51 for I2 in the -x -direction, with all the other quantities the same.

Name: Problem 52, Chapter 28: University Physics with Modern Physics In SI Units
Uploaded: 2021-04-20T15:36:04-08:00
Duration: 5 min 57 s
Channel: Vishal Gupta
Description: -? Repeat Problem 28.51 for I2 in the -x -direction, with all the other quantities the same.

-? Repeat Problem 28.51 for I2 in the -x -direction, with...

Key Concepts

Biot?Savart Law

The Biot?Savart law is a fundamental principle that gives the magnetic field produced by a small current element. It requires integrating the contributions from every current element in a conductor, considering both the distance from the element to the point where the field is evaluated and the angle between the current element and the position vector. This law is essential when calculating magnetic fields generated by various current configurations.

Superposition Principle in Electromagnetism

The superposition principle states that the net magnetic field created by multiple current elements is the vector sum of the fields due to each individual element. This principle allows one to treat complex current distributions by breaking them down into simpler parts, solving for each part, and then summing their contributions, while taking into account any changes in direction or other parameters.

Right?Hand Rule and Vector Direction

The right?hand rule helps determine the direction of the magnetic field produced by a current. When the current flows in a given direction, the thumb points in the direction of the current, and the curled fingers show the direction of the magnetic field. Changing the current’s direction (for example, from the positive to the negative x-direction) reverses the corresponding magnetic field directions, making it an important concept in analyzing the vector nature and sign conventions of magnetic fields.

Transcript

00:01 Hi, in the given problem there are two straight parallel current carrying conductors.

00:09 One of the conductor has been kept along the x -axis, which is carrying a current i -1 in the direction of positive x -axis and the another conductor which has been kept.

00:27 Having a position y is equal to 0 .800 meter means the gap between these two parallel current carrying conductors is 0 .8 0 meter and the direction of current in it is along negative x -axis so this is i 2 along negative x -axis and this is i 1 along positive x -axis having the magnitudes i 1 is equal to 2 .00 ampere and and i 2 is equal to 6 .00 ampere now we have to find the position we have to find the position of a point at which the net magnetic field due to these two current carrying conductors should be zero so using right hand thumb rule we conclude that the direction of magnetic field direction of magnetic fields due to both of the conductors will be outward perpendicular to the plane of paper at every point between the conductors so will be added to give a non -zero magnetic field means the magnet field cannot be zero at any point between the conductors so suppose the magnetic field net magnetic field is 0 at a point p at a distance y from the second conductor suppose because at that point the magnetic fields will be opposite in direction so there is a chance to have the same magnitude hence the net magnetic field will come out to be 0 so suppose the net magnetic field is 0 at a point is 0 at a point point p which is distanced y from the second conductor so we can say using bytend seward's law the expression for magnetic field due to a straight current carrying conductor is means this b at p due to one will be having the same magnitude that of b at p due to the conductor two and since we can say this is mu not by 4 pi into 2 i1 divided by y plus 0 .80 meter is equal to mu not by 4 pi into 2 i2 divided by just y so canceling this mu not by 4 pi and 2 from both the sides and plugging in the values of i 1 and i 2 for i 1 this is 2 ampere 2 .00 ampere divided by y plus 0 .8 0 .0 meter is equal to i2 which is 6 .00 amper divided by y so canceling this ampere and 6 will be cancelled by 2 giving just a 3 and then making a cross multiplication we get y is equal to 3y plus 2 .4 so here it will come out to be minus minus 2y is equal to 2 .4 or we can say this distance y is equal to minus 1 .2 meter.

04:54 Means this negative sign is representing that the position of this point is opposite in direction...

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