Four infinite thin current carrying sheets are placed in Y-Z plane. The 2D view of the arrangement is as shown in Fig. Direction of current has alos been shown in the figure. The linear current density, i.e., current per unit width in the four sheets are I, 2I, 3I, and 4I, respectively.

Options

A.
B.
C.
D.

Answer

C

Explanation

(c) Magnetic field due to infinite current carrying sheet is given
by `B=(mu_0I)/2`, where I is linear current density.
For `xlta, B_("resultant")=(mu_0I)/2-(mu_0 (2I))/2-(mu_0 (3I))/2+(mu_0 (4I))/2=0`
For `altxlt2a`,
`B_("resultant")=-(mu_0I)/2-(mu_0 (2I))/2-(mu_0 (3I))/2+(mu_0 (4I))/2=-mu_0I`
For `2altxlt3a`,
`B_("resultant")=-(mu_0I)/2+(mu_0 (2I))/2-(mu_0 (3I))/2+(mu_0 (4I))/2=mu_0I`
For `4altx`,
`B_("resultant")=(-mu_0I)/2+(mu_0 (2I))/2+(mu_0 (3I))/2+(mu_0 (4I))/2=4mu_0I`
For `xgt4a, B_("resultant")=0`