1. Field due to a single infinite charged sheet

For an infinite plane sheet with surface charge density $\sigma$, the electric field has magnitude

$E = \frac{|\sigma|}{2\varepsilon_0}$

on each side of the sheet.

• For a positive sheet, field lines go away from the sheet.
• For a negative sheet, field lines go towards the sheet.

So each sheet produces a uniform field in the regions around it.

2. Geometry of the problem

Two infinite sheets intersect at right angle. Let us take:

• one sheet as the plane $x=0$ with charge density $\sigma_+$,
• the other sheet as the plane $y=0$ with charge density $\sigma_-$.

They divide space into four regions in the $xy$-cross section.

Let

$E_+ = \frac{|\sigma_+|}{2\varepsilon_0}, \qquad E_- = \frac{|\sigma_-|}{2\varepsilon_0}$

with

$E_+ > E_-$

because $|\sigma_+| > |\sigma_-|$.

3. Direction of fields from each sheet

Field due to the positive sheet ($x=0$)

Since it is positive, field is away from the sheet:

• for $x>0$: along $+\hat i$
• for $x<0$: along $-\hat i$

Field due to the negative sheet ($y=0$)

Since it is negative, field is towards the sheet:

• for $y>0$: along $-\hat j$
• for $y<0$: along $+\hat j$

4. Net electric field in each region

Add the two perpendicular uniform fields.

Region I: $x>0, y>0$

$\vec E = E_+\hat i - E_-\hat j$

This points right and slightly downward.

Region II: $x<0, y>0$

$\vec E = -E_+\hat i - E_-\hat j$

This points left and downward.

Region III: $x<0, y<0$

$\vec E = -E_+\hat i + E_-\hat j$

This points left and slightly upward.

Region IV: $x>0, y<0$

$\vec E = E_+\hat i + E_-\hat j$

This points right and upward.

5. Nature of field lines

Since in each region the net field is constant, the field lines in each region are straight lines. Their direction is determined by the vector sum above.

Because $E_+ > E_-$, the horizontal component is larger than the vertical component, so the field lines are inclined more toward the effect of the positive sheet.

Also:

• field lines must originate from the positive sheet,
• and terminate on the negative sheet.

Thus the correct sketch should show straight field lines in the four regions, tilted such that they go from the $+$ sheet toward the $-$ sheet, with greater horizontal than vertical component.

6. Matching with options

Among the given options, the diagram satisfying these conditions is Option B.

7. Comparison with stored answer

Derived answer: B

Stored correct answer: B

They agree.