Question

Find the position of point from wire 'B' where net magnetic field is zero due to following current distribution

• A. 4 cm
• B. $\frac { 30 } { 7 } \mathrm {~cm}$
• C. $\frac { 12 } { 7 } \mathrm {~cm}$
• D. 2 cm

Answer 1

Answer: (C)

$\frac { 12 } { 7 } \mathrm {~cm}$

Answer 2

Suppose P is the point between the conductors where net magnetic field is zero.

So at P |Magnetic field due to conductor 1| = |Magnetic field due to conductor 2|

i.e. $\frac { \mu _ { 0 } } { 4 \pi } \cdot \frac { 2 ( 5 i ) } { i } = \frac { \mu _ { 0 } } { 4 \pi } \cdot \frac { 2 ( 2 i ) } { ( 6 - x ) }$⇒ $\frac { 5 } { x } = \frac { 9 } { 6 - x }$

⇒ $x = \frac { 30 } { 7 } \mathrm {~cm}$

Hence position from B $= 6 - \frac { 30 } { 7 } = \frac { 12 } { 7 } \mathrm {~cm}$