Question

Two parallel long wires carry currents i1 and i2 with i1 > i2. When the currents are in the same direction the magnetic field at a point midway between the wires is 10 micro tesla. If the direction of i2 is reversed ,the field becomes 30 micro tesla. What is the ratio of i1/i2 ??

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Answer 1

Magnetic field at perpendicular distance x from a long wire carrying current i is $B=\frac{\mu_0i}{2\pi x}$

we know, current through two parallel long wires are in same direction then, magnetic field at the midpoint of parallel wires is $B=B_1-B_2$

Let (2d) is separation between two parallel wires.

so, $B=\frac{\mu_0i_1}{2\pi d}-\frac{\mu_0i_2}{2\pi d}$

given, B = 10$\mu T$

so, $10=\frac{\mu_0}{2\pi d}(i_1-i_2)$........(1)

current through two parallel long wires are in opposite directions then, magnetic field at the midpoint of parallel wires is $B'=B_1+B_2$

or, $B'=\frac{\mu_0i_1}{2\pi d}+\frac{\mu_0i_2}{2\pi d}$

given, B' = 30$\mu T$

so, $30=\frac{\mu_0}{2\pi d}(i_1+i_2)$.......(2)

from equations (1) and (2),

$\frac{10}{30}=\frac{(i_1-i_2)}{(i_1+i_2)}$

or,$\frac{1}{3}=\frac{\frac{i_1}{i_2}-1}{\frac{i_1}{i_2}+1}$

or,$\frac{i_1}{i_2}+1=3\frac{i_1}{i_2}-3$

or,$4=2\frac{i_1}{i_2}$

or,$\frac{i_1}{i_2}=2$

Answer 2

Answer:

I1/I2 = 2

Explanation:

when both the current are in the same direction then

let 2d is the distance between both the wire and magnetic field for infinite long rod is munot I/ 2PID

let the midway point is p

so when the current I1 and I2 are in the same direction let it be in upward direction

so direction of magnetic field due to I1 is cross that means inward and due to I2 field is dot that means inward

magnetic field at point p = mu not(I1-I2)/2pid = 1*10^-3

we can multiply this equation by 3

so we get 3munot(I1-I2)/2pid=30*10^3

now if we change the direction of I2 current let it be in downward direction

so direction of magnetic field due to both the wire is cross that means inward to the plane

so now magnetic field at p is munot (i1+i2)/2pid = 30 *10^3

compare both the bold equation

we get

3(I1-I2)= I1+I2

I1 = 2I2

I1/I2 = 2

hope it is helpful.......................