The drawing shows two long, straight wires that are...

Name: The drawing shows two long, straight wires that are suspended from a ceiling. The mass per unit length of each wire is 0.053 kg/m. Each of the four strings suspending the wires has a length of 1.20 m. When the wires carry identical currents in opposite directions, the angle between the strings holding the two wires is 15.0°. What is the current in each wire? (g = 9.80 m/s²)
Uploaded: 2021-10-10T02:28:51-08:00
Duration: 6 min 13 s
Channel: Nishant Kumar
Description: The drawing shows two long, straight wires that are suspended from a ceiling. The mass per unit length of each wire is 0.053 kg/m. Each of the four strings suspending the wires has a length of 1.20 m. When the wires carry identical currents in opposite directions, the angle between the strings holding the two wires is 15.0°. What is the current in each wire? (g = 9.80 m/s²)

The drawing shows two long, straight wires that are suspended from a ceiling. The mass per unit length of each wire is 0.053 kg/m. Each of the four strings suspending the wires has a length of 1.20 m. When the wires carry identical currents in opposite directions, the angle between the strings holding the two wires is 15.0°. What is the current in each wire? (g = 9.80 m/s²)

Transcript

00:02 Here we have two long straight wires that are suspended from a ceiling and we have to find the current in each wire which is the same in magnitude but opposite in direction so we draw the front face of the two wires this is wire one this is wire two and this is the tension t in the string the combined tension in the two strings which is attached to this wire and the total angle is 15 degree so this angle theta will be 15 upon 2 equal to 7 .5 degree so this tension angle with vertical will also be theta and the magnetic force from the other wire will be repulsive so it will be away from the other wire it is called this force f and downward force is mg which is the weight now in vertical direction we will take upper direction as positive so the net force in vertical direction is t cost theta upper direction minus mg downward direction and this would be zero because there is no acceleration so some of the vertical forces will be zero so t equal to m g upon cost theta.

01:54 Now in a horizontal direction, we will take the direction to the right as positive.

02:07 So magnetic force f minus t sine theta, which is the component of tension to the left, will be equal to zero because there is no acceleration in horizontal direction.

02:20 So f is equal to t sine theta.

02:29 From here we can write f equal to in place of t we write m g upon cost theta so f is equal to m g tan theta now magnetic force is mu one sorry mu not i1 i2 but both currents are same in magnitude so it will be simply i square upon 2 pi d d is the distance between the two wires multiplied by the length of wire l and it will be equal to mg tan theta now this distance is d between the wires so it will be d upon 2 and d upon 2 and this length is given 1 .2 meter let us call it l the length of the strings so d upon 2 is equal to l sine theta d upon 2 is equal to l sine theta so d is equal to 2 l sine theta so we put the value mu not i square l from 2 pi 2 l sine theta now on the right hand side we have m g tan theta now the mass per unit length of wire is given...

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