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`.

Explanation

Net electric field is `vecP`
`vecE=vecE_(1)+vecE_(2)` due to vertical wire
`vecE_(1)=(lamda_(1))/(2piepsilon_(0)y)` I `+y`-direction
`vecE_(2)=(lamda_(2))/(2piepsilon_(0)x)` due to vertical wire in x-direction
`tanalpha=(E_(1))/(E_(2))=(lamda_(1)//2piepsilon_(0)y)/(lamda_(2)//2piepsilon_(0)x)`
or `(1)/(sqrt(3))=(lamda_(1)x)/(lamda_(2)y)` or `(lamda_(1))/(lamda_(2))=(x)/(y)sqrt(3)` or `(lamda_(1))/(lamda_(2))=3`