Question

Two straight long conductors AOB and COD are perpendicular to each other and carry currents I₁and I₂. The magnitude of the magnetic induction at a point P at a distance d from the point O in a direction perpendicular to the plane ABCD is –

• A. $\frac { \mu _ { 0 } } { 2 \pi d }$ (I₁ + I_­2)
• B. $\frac { \mu _ { 0 } } { 4 \pi d }$ (I₁ – I₂)
• C. $\frac { \mu _ { 0 } } { 2 \pi d }$
• D. $\frac { \mu _ { 0 } } { 2 \pi d }$

Answer 1

Answer: (C)

$\frac { \mu _ { 0 } } { 2 \pi d }$

Answer 2

At P there are two fields

(1) B₁ = due to AOB = $\frac { \mu _ { 0 } \mathrm { i } _ { 1 } } { 2 \pi \mathrm { d } }$ (+ y)

(2) B₂ = due to COD = (– x)

\ B = $\sqrt { \mathrm { B } _ { 1 } ^ { 2 } + \mathrm { B } _ { 2 } ^ { 2 } }$