Question 205: Magnetism and Matter

Question

Two wires A & B are carrying currents I
1
& I
2
as shown in the figure. The separation between
them is d. A third wire C carrying a current I
is to be kept parallel to them at a distance x from
A such that the net force acting on it is zero.
The possible values of x are :
![](https://imagex.cdn.examgoal.net/3rsa0w2w9jwyu2kec/34e09438-ee30-4653-91bc-41f19f26798f/3621b840-9025-11e9-86c1-73f7f991b766/file-3rsa0w2w9jwyu2ked.png)

Accepted Answer

Net force on wire carrying current I per unit
length is
${{{\mu _0}{I_1}I} \over {2\pi x}} + {{{\mu _0}{I_2}I} \over {2\pi \left( {d - x} \right)}} = 0$
${{{I_1}} \over x} = {{{I_2}} \over {x - d}}$
$ \Rightarrow x = {{{I_1}d} \over {{I_1} - {I_2}}}$

Answer

$x = \left( {{{{I_1}} \over {{I_1} + {I_2}}}} \right)d\,and\,x = \left( {{{{I_2}} \over {{I_1} - {I_2}}}} \right)d$

Answer

$x = \left( {{{{I_2}} \over {{I_1} + {I_2}}}} \right)d\,and\,x = \left( {{{{I_2}} \over {{I_1} - {I_2}}}} \right)d$

Answer

$x = \left( {{{{I_1}} \over {{I_1} - {I_2}}}} \right)d\,and\,x = \left( {{{{I_2}} \over {{I_1} + {I_2}}}} \right)d$

Answer

$x =  \pm {{{I_1}d} \over {{I_1} - {I_2}}}$

Magnetism and Matter

Two wires A & B are carrying currents I 1 & I 2 as shown in the figure. The separation between them is d. A third wire C carrying a current I is to be kept parallel to them at a distance x from A such that the net force acting on it is zero. The possible values of x are :

Choose the correct answer: