Two wires parallel to each other and seperated by a distance d carry different c

Question

Two wires parallel to each other and seperated by a distance d carry different currents; they exert a force with magnitude F on each other.
(a) The wires carry current in opposite directions. If the current carried by both wires is tripled and the distance between the wires is divided by five, then what will the force's magnitude be (as a multiple of F) and will it be repulsive or attractive? (F)

---Select--- attractive or repulsive

(b) The wires carry current in the same direction . If the current carried by one of the wires is quadrupled and the distance between the wires is divided by three, then what will the force's magnitude be (as a multiple of F) and will it be repulsive or attractive? (F)

---Select--- attractive or repulsive

Thank you for your help!

Explanation / Answer

given that

distance b/w the wirers is d.

we know that

Formula

F = uo*I1*I2 /2*pi*d

from the above formula we can

see that the force is proportional to

the product of the currents and

inversely proportional to the

distance between the wires.

(a)

in this case

d' = 5*d

I1' = I1/5

so

F1 = uo*I1/5*I2 /2*pi*5*d

F1 = F/25------ans

The force is attraction if the currents are in the same direction and repulsion if the

cureents are in opposite directions.

here currents in opposite direction

so force is repulsive.

(b)

in this case

I1' = I1/3

I2' = I2/3

d' = 4*d

so

F2 =(uo*I1/3*I2/3) / 2*pi*4*d

F2 = F/36--------ans

The force is attraction if the currents

are in the same direction and

repulsion of the cureents are in opposite directions.

here direction of current is

same so force attractive.

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