Question

Two parallel long wire carry i1 and i2 with i1 >i2 . When the current are in the same direction , the magnetic field at a point midway between the wires is 10 micro T. If the direction of i2 is reversed ,the field becomes 3micro T . The ratio of i1/i2 is (1)4. (2)3 (3)2. (4)1

Answer 1

Answer on Question #74648 Physics / Electromagnetism

Two parallel long wire carry $I_{1}$ and $I_{2}$ with $I_{1} > I_{2}$. When the current are in the same direction, the magnetic field at a point midway between the wires is $10~\mu \mathrm{T}$. If the direction of $I_{2}$ is reversed, the field becomes $30~\mu \mathrm{T}$. The ratio of $I_{1} / I_{2}$ is:

(1)4.

(2)3

(3)2.

(4)1.

Solution:

The magnetic field at the distance $r$ from the long wire with current $I$ is as follow

$$B = \frac {\mu_ {0} I}{2 \pi r}.$$

When the current are in the same direction, net magnetic field

$$B = B _ {1} - B _ {2} = \frac {\mu_ {0} I _ {1}}{2 \pi d} - \frac {\mu_ {0} I _ {2}}{2 \pi d} = 1 0 \mu \mathrm {T}$$

When the current are in the opposite direction, net magnetic field

$$B = B _ {1} + B _ {2} = \frac {\mu_ {0} I _ {1}}{2 \pi d} + \frac {\mu_ {0} I _ {2}}{2 \pi d} = 3 0 \mu \mathrm {T}$$

So

$$\frac {I _ {1} - I _ {2}}{I _ {1} + I _ {2}} = \frac {1 0}{3 0}$$ $$3 0 I _ {1} - 3 0 I _ {2} = 1 0 I _ {1} + 1 0 I _ {2}$$ $$2 0 I _ {1} = 4 0 I _ {2}$$ $$\frac {I _ {1}}{I _ {2}} = 2$$

Answer: (3) 2

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