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 #74649, Physics / Electromagnetism

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 30 microT. The ratio of i1/i2 is (1)4. (2)3 (3)2. (4)1.

Answer:

$$B = \frac {\mu_ {0} i}{2 \pi d}$$

Magnetic field due to the two current carrying wire in the same direction

$$B _ {n e t} = B _ {1} - B _ {2}$$

Where

$$B _ {1} = \frac {\mu_ {0} i _ {1}}{2 \pi d}$$

and

$$B _ {2} = \frac {\mu_ {0} i _ {2}}{2 \pi d}$$

So

$$B _ {n e t} = \frac {\mu_ {0} i _ {1}}{2 \pi d} - \frac {\mu_ {0} i _ {2}}{2 \pi d}$$

or

$$1 0 = \frac {\mu_ {0}}{2 \pi d} \left(i _ {1} - i _ {2}\right) \dots \dots \dots (1)$$

Magnetic field due to the two current carrying wire in the direction of i2 is reversed

$$B _ {n e t} = B _ {1} + B _ {2}$$ $$B _ {n e t} = \frac {\mu_ {0} i _ {1}}{2 \pi d} + \frac {\mu_ {0} i _ {2}}{2 \pi d}$$

or

$$3 0 = \frac {\mu_ {0}}{2 \pi d} \left(i _ {1} + i _ {2}\right) \dots \dots \dots (2)$$

Dividing 1 by 2. We have

$$\frac {1}{3} = \frac {\left(i _ {1} - i _ {2}\right)}{\left(i _ {1} + i _ {2}\right)} \quad (i _ {1} + i _ {2}) = 3 \left(i _ {1} - i _ {2}\right)$$

Finally, we get

$$2 i _ {1} = 4 i _ {2}$$ $$\frac {i _ {1}}{i _ {2}} = \frac {4}{2} = 2$$

Answer: 2

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