An arrangement of three parallel straight wires placed perpendicular to plane of paper carrying same current along the same direction as shown in figure. Magnitude of force per unit length on the middle wire is given by [2017]

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Q.
An arrangement of three parallel straight wires placed perpendicular to plane of paper carrying same current $' I'$ along the same direction as shown in figure. Magnitude of force per unit length on the middle wire $‘ B ’$ is given by [2017]

1 $\frac{2 μ_{0} I^{2}}{π d}$

2 $\frac{\sqrt{2} μ_{0} I^{2}}{π d}$

3 $\frac{μ_{0} I^{2}}{\sqrt{2} π d}$

4 $\frac{μ_{0} I^{2}}{2 π d}$

Ans.
(3)

Force between wires A and B = force between wires B and C

$∴$    $F_{B C} = F_{A B} = \frac{μ_{0} I^{2} l}{2 π d}$

As,   ${\vec{F}}_{A B} ⊥ {\vec{F}}_{B C}$ net force on wire B,

$F_{net} = \sqrt{2} F_{B C} = \frac{\sqrt{2} μ_{0} I^{2} l}{2 π d}$

or   $\frac{F_{net}}{l} = \frac{μ_{0} I^{2}}{\sqrt{2} π d}$

Solution

Q.
An arrangement of three parallel straight wires placed perpendicular to plane of paper carrying same current $' I'$ along the same direction as shown in figure. Magnitude of force per unit length on the middle wire $‘ B ’$ is given by [2017]

1 $\frac{2 μ_{0} I^{2}}{π d}$

2 $\frac{\sqrt{2} μ_{0} I^{2}}{π d}$

3 $\frac{μ_{0} I^{2}}{\sqrt{2} π d}$

4 $\frac{μ_{0} I^{2}}{2 π d}$

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Solution

Q. An arrangement of three parallel straight wires placed perpendicular to plane of paper carrying same current 'I' along the same direction as shown in figure. Magnitude of force per unit length on the middle wire ‘B’ is given by [2017]

1 2μ0I2πd

2 2μ0I2πd

3 μ0I22πd

4 μ0I22πd

Ans. (3) Force between wires A and B = force between wires B and C ∴ FBC=FAB=μ0I2l2πd As, F→AB⊥F→BC net force on wire B, Fnet=2FBC=2μ0I2l2πd or Fnetl=μ0I22πd

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Q.
An arrangement of three parallel straight wires placed perpendicular to plane of paper carrying same current $' I'$ along the same direction as shown in figure. Magnitude of force per unit length on the middle wire $‘ B ’$ is given by [2017]

1 $\frac{2 μ_{0} I^{2}}{π d}$

2 $\frac{\sqrt{2} μ_{0} I^{2}}{π d}$

3 $\frac{μ_{0} I^{2}}{\sqrt{2} π d}$

4 $\frac{μ_{0} I^{2}}{2 π d}$