Two long, parallel wires carry currents of I1 = 2.88 A and I2 = 4.75 A in the di

Question

Two long, parallel wires carry currents of I1 = 2.88 A and I2 = 4.75 A in the direction indicated in the figure below. (Choose the line running from wire 1 to wire 2 as the positive x-direction and the line running upward as the positive y-direction.)

(a) Find the magnitude and direction of the magnetic field at a point midway between the wires (d = 20.0 cm).
magnitude µT
direction ° (counterclockwise from the +x-axis)

(b) Find the magnitude and direction of the magnetic field at point P, located d = 20.0 cm above the wire carrying the 4.75-A current.
magnitude µT
direction ° (counterclockwise from the +x-axis)

Explanation / Answer

WELL SIR I CANNOT SEE THE FIGURE BUT I WILL TRY TO PROVIDE YOU EACH ANALYSIS

magnetic field due to a long current carrying wire is given by :
B = 0i/2r

where r is the distance of point where we want to find the magnetic field

B1 = 0i1/2d
     = 2 * 9 * 109 * 2.88 / 10 * 10-2
     = 51.84 * 1010 T

B2 = 0i2/2d
    = 2 * 9 * 109 * 4.75 / 10 * 10-2
     = 85.5 * 1010 T

direction will determine whether these two fields will be added or subtracted.

IF THE CUURENTS ARE MOVING PARALLEL TO EACH OTHER THEN
using right hand thumb rule which states that if we align our thumb in the direction of moving current then our curling fingers gives the diection of magnetic field
B = B1 - B2
   = (51.84 - 85.5) * 1010
   = |-33.66 * 1010 | T
   = 33.66 * 1010

well direction of this field be in according with whether B2 is clockwise or anti clockwise


IF THE CURENTS ARE MOVING ANTI-PARALLEL TO EACH OTHER THEN
B = B1 + B2
   = (51.84 + 85.5) * 1010
   = |137.34* 1010 | T
   = 137.34 * 1010 T

well direction of this field be in according according to the direction of currents in the two wires


(b) magnetic field B3 = 0i2/2g
    B3 = 85.5 * 1010 / 2
        = 42.75 * 1010 T

distance of point P from other wire = sqrt(202 + 202 ) = 202 cm
B4 = 0i2/2g1
    = 2 * 9 * 109 * 2.88 / 202 *10-2
    = 18.32 * 1010 T

PARALLEL :
B = |B3 - B4|
   = 24.43 *1010 T
DIRECTION ACCORDINGLY

anti-PARALLEL :
B = |B3 + B4|
   = 61.07 *1010T
DIRECTION ACCORDINGLY

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