Question

Four very long, current carrying wires in the same plane intersect to form a square $40.0cm$ on each side, as shown in figure. find the magnitude and direction of the current $I$ so that the magnetic field at the center of the square is zero.

• A. $4.0A$ toward the bottom of the page
• B. $2.0A$ toward the bottom of the page
• C. $2.5A$ toward the bottom of the page
• D. $3.6A$ toward the top of the page

Answer 1

The correct option is B $2.0A$ toward the bottom of the page

$B\propto I$, because distance of centre for all wires is zero.

$B_1=K{I}_1=10k⨂,B_2=k{I}_2=8k⨂$

$B_3=k{I}_3=20k⨀,B_4=k{I}_4$

Now $B_1+B_2+B_3+B_4=0$

$\Rightarrow (10k+8k-20k)⨂+k{I}_4=0$

$\Rightarrow k{I}_4=2k⨂$

$\Rightarrow k{I}_4=2A$ towards bottom