An arrangement of three parallel straight wir | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The force per unit length between two parallel wires carrying current $I$ separated by distance $d$ is given by $f = \frac{{\mu _0}{I^2}}{2{\pi d}

Vedclass · Accepted Answer

$\frac{{\mu _0}{I^2}}{{\sqrt 2 \pi d}}$

Vedclass · Answer

(C) The force per unit length between two parallel wires carrying current $I$ separated by distance $d$ is given by $f = \frac{{\mu _0}{I^2}}{2{\pi d}}$.Since the currents are in the same direction,the force is attractive.Wire $B$ experiences an attractive force $F_{AB}$ towards wire $A$ and an attractive force $F_{BC}$ towards wire $C$.The magnitudes are $F_{AB} = F_{BC} = \frac{{\mu _0}{I^2}}{2{\pi d}}$ (per unit length).Since the wires are arranged at a $90^{\circ}$ angle,the vectors $\vec{F}_{AB}$ and $\vec{F}_{BC}$ are perpendicular to each other.The net force per unit length $f_{	ext{net}}$ is the vector sum: $f_{	ext{net}} = \sqrt{F_{AB}^2 + F_{BC}^2} = \sqrt{2} F_{BC}$.Substituting the value: $f_{	ext{net}} = \sqrt{2} \left( \frac{{\mu _0}{I^2}}{2{\pi d}} ight) = \frac{{\mu _0}{I^2}}{{\sqrt 2 \pi d}}$.

An arrangement of three parallel straight wires placed perpendicular to the plane of the paper carrying the same current $I$ along the same direction is shown in the figure. The magnitude of the force per unit length on the middle wire $B$ is given by:

Similar Questions

$P, Q$ and $R$ are long parallel straight wires in air,carrying currents $20 \ A, 40 \ A$ and $60 \ A$ as shown in the figure. What is the direction of the resultant force on $Q$?

The force acting on a current-carrying wire joining two fixed points $A$ and $B$ in a uniform magnetic field is:

Three long straight wires are connected in parallel to each other across a battery of negligible internal resistance. The ratio of their resistances is $3 : 4 : 5$. What is the ratio of the distances of the middle wire from the others if the net force experienced by it is zero?

Vedclass Test Series

Exam Paper Generator

Online Exam Module