- - Two parallel wires are 5.80 cm apart and carry currents in opposite directions, as shown in

step 1 Hi. Here in this given problem there are two parallel wires. The long wires of infinite length,

- - Two parallel wires are 5.80 cm apart and carry currents...

- - Two parallel wires are $5.80 \mathrm{~cm}$ apart and carry currents in opposite directions, as shown in Fig. E28.12. Find the magnitude and direction of the magnetic field at point $P$ due to two $1.50 \mathrm{~mm}$ segments of wire that are opposite each other and each $8.00 \mathrm{~cm}$ from $P$.

Key Concepts

Right-Hand Rule

This is a mnemonic used to determine the direction of the magnetic field around a current-carrying conductor. By pointing the thumb of the right hand in the direction of the conventional current, the curled fingers indicate the direction of the magnetic field lines encircling the conductor. This concept is crucial for determining the orientation of the fields produced by different segments of current-carrying wires, especially when currents have opposite directions.

Superposition Principle

The magnetic field at any point due to multiple sources is the vector sum of the individual fields produced by each source. In problems involving multiple wire segments or different sections of current-carrying conductors, the overall magnetic field is found by calculating each contribution separately and then combining them according to their directions and magnitudes.

Biot?Savart Law

This law provides the fundamental relation for calculating the magnetic field generated at a point in space due to a small current element. The law shows that each infinitesimal segment of current contributes to the magnetic field at a point and that this contribution depends on the current, the distance from the element to the point, and the sine of the angle between the current element and the position vector. It lays the groundwork for integrating these contributions over the length of a current-carrying conductor, particularly when the conductor is not infinitely long.

Magnetic Field from a Finite Current Segment

Unlike infinitely long wires where Ampère's law can be directly applied, finite segments require the evaluation of the integrated contributions from the Biot?Savart law over the finite length of the wire. This involves summing the effects of current elements along the length of the wire, taking into account the geometry and the angles subtended by the endpoints of the segment relative to the point where the field is calculated.

Transcript

0:00 Hi.

00:01 Here in this given problem there are two parallel wires.

00:05 The long wires of infinite length, the upper wire carrying a current i1 is equal to 12 .0 amp towards right and the lower wire that is carrying the current i2 is equal to 24 .0 ampere towards left.

00:31 The total gap between them, if we assume it to be d, that gap is given as 5 .80 centimeter.

00:46 There is a point midway between the two wires, p, and the two current carrying elements of same length directly opposite to each other.

01:03 Each having a length 1 .50 millimeter and we have to find net magnetic field due to these two elements at the point p.

01:24 So we join current elements with the observation point p.

01:34 Now the directions of the currents, this is towards right and direction of position vector that is like this for the first element.

01:52 And for the second element, this is the direction of current towards left and the direction of position vector this.

02:03 So as far as the angle is concerned, for the upper element, this will be the acute angle, theta.

02:10 And for the lower current element this will be the angle using linear pair that will be 180 degree minus theta and as the observation point is midway between the two wires so these lengths equal to half of d means 5 .80 by 2 means this is 2 .90 centimeter for each wire and the distance of observation point this from the current element are that is given as 8 .00 centimeter from there to there 8 .00 centimeter for both the elements okay so using the rules of parallel lines if this angle is theta, this angle will also be theta...

Please give Ace some feedback