Two mutually perpendicular infinite wires along x-axis and y-axis carry charge densities `lambda_1 and lambda_2`. The electric line of force at P is along the line `y = x//(sqrt3)`, where P is also a point lying on the same line. Find `lambda_2//lambda_1`.

Answer

C

Explanation

Net electric field is `overline p, vecE=vecE_1+vecE_2` due to vertical wire
`vecE_2=lamda_2/(2 pi e_0 x)` due to vertical wire in x-direction, a angle of electric field with x direction
`tan a =E_1/E_2 =(lamda_1//2 pi e_0 y)/(lamda_2//2 pi e_0x) or 1/sqrt3 = (lamda_1x)/(lamda_2y) or lamda_2/lamda_1=x/y sqrt3 or lamda_2/lamda_1=3`