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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`. |
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Answer» 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` |
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