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Two long straight parallel wieres are 2m...

Two long straight parallel wieres are `2m` apart, perpendicular to the plane of the paper. The wire A carries a current of `9.6 A`, directed into the plane of the paper. The wire `B` carries a current such that the magnetic field of induction at the point `P`, at a distance of `10/11` m from the wire B, is zero. find
a. the magnitude and directiion of the current in B.
b. the magnitude of the magnetic field of induction of the pont `S`.
c. the force per unit length on the wire `B`.

Text Solution

Verified by Experts

a. Direction of current at `B` should be perpendicular to paper outwards. Let curent in this wire be `i_B`. Then
`mu_0/(2pi) i_A/((2+10/11))=mu_0/(2pi) i_B/((10/11))`
or `i_B/i_A=10/32`
or `i_B=10/32xxi_A=10/32x9.6=3A`
b. Since `AS^2+BS^2+AB^2`
`/_ASB=90^@`
At `S:B_1=` Magnetic field due to `i_A`
`=mu_0/(2pi) i_A/1.6=((2xx10^I-7)(9.6))/1.6`
`=12xx10^-7T`
`B_2=`magnetic field to due to `i_B`
`=mu_0/(2pi) i_B/1.2`
`=((2xx10^i-7)(3))/1.2`
`=5xx10^-7T`
Since `B_1 and B_2` are mutually perpedicular.Net magnetic field at S would be
`b=sqrt(B_1^2+B_2^2)`
`=sqrt((12xx106i-7)^2+(5xx10^-7)^2)`
`=13xx10^-7T`
c. Force per unit length on wire B:
`F/l=mu_0/(2pi)(i_Ai_B)/r` `[:.r=AB=2m]`
`=((2xx10^-7)(9.6xx3))/2`
`=2.88xx10^I-6N/m`
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