KVPY SX SB Exam 2016 Question Paper

Question : 40 of 120

Marks: +1, -0

Two infinitely long parallel wires carry currents of magnitude

I_1

and

I_2

and are at a distance 4 cm apart. The magnitude of the net magnetic field is found to reach a non-zero minimum values between the two wires and 1 cm away from the first wire. The ratio of the two currents and their mutual direction is

$I_2/I_1= 9$ , antiparallel
$I_2/I_1= 9$ , parallel
$I_2/I_1= 3$ , antiparallel
$I_2/I_1= 3$ , parallel

Validate

Solution:

B_p={µ_0I_1}/{2πx}+{µ_0I_2}/{2π(4-x)}

{dB_p}/{dx}=0

for minima of

B_p

⇒{µ_0I_1}/{2π}[-1/x^2]+

{µ_0I_2}/{2π}1/(4-x)^2=0

I_1/I_2=(x/{4-x})^2

I_1/I_2=(1/{4-1})^2

I_2/I_1=9/1

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