Question

Two parallel conductors carrying current of 4.0 A and 10.0 A are placed 2.5 cm apart in vacuum. The force per unit length between them is - (a) 6.4 x 10-5 N/m 6.4 x 10-2 Nm (b) (c) 4.6 x 10-4 N/m (d) 3.2 x 10-4 N/m 84102, 841152​

Answer 1

Answer:

Two parallel conductors carrying a current of 4.0 A and 10.0 A are placed 2.5 cm apart in a vacuum. The force per unit length between the two conductors is $3.2*10^{-4}N/m$

Explanation:

• From the Biot-Savart law, we know there will be a magnetic field due to current-carrying conductors, that magnetic field exerts a force on the conductor

• suppose that a conductor A with  current $I_{A}$ and another conductor B carrying current $I_{B}$ are separated by a distance $r$ the force on a length $L$ of the conductor A due to conductor B is

                                 $F_{AB}=I_ALB_{B}$

• From Ampere's law, the magnetic field at the conductor B is

                                $B_{B}=\mu _0I_B/2\pi r$

• so the force between the conductors

                                $F_{AB}=\mu _0I_BI_{A} L/2\pi r$

from the question, we have

current in conductor A $I_{A}=4A$

and that of conductor B is $I_{B} =10A$

the distance between the conductors $r=2.5cm=0.025m$

asked for force per unit length $L=1m$

value of $\mu _0=4\pi *10^{-7}$

⇒

$F_{AB}=\frac{4\pi *10^{-7} *4*10}{2\pi *0.025} =3.2*10^{-4}N/m$

Answer 2

Given :

current in conductor 1 (i$_{1}$) = 4 A; current in conductor 2 (i$_{2}$) = 10 A; Distance between the conductors (d) = 2.5 cm = 2.5 x $10^{-2}$ m

To Find :

The force per unit length between the current carrying conductors

Solution :

Force per unit length ($\frac{dF}{dL}$) = $\frac{u_{0} }{4\pi } \frac{2i_{1} i_{2} }{d}$

                                          =  $10^{-7}$ × $\frac{2 * 4 * 10}{2.5 *10^{-2} }$

                                          = 32 x $10^{-5}$

                                          = 3.2 x $10^{-4}$ N/m

Therefore, The force per unit length between the conductors is 3.2 x $10^{-4}$ N/m.

The correct option is (d).

Note -

• It is the mutual interaction.
• Parallel currents in same direction attract each other.
• Current in opposite direction repel each other.