Question

Two mutually perpendicular infinite wires along x axis and y axis carry charge densities l1 and l2. the
electric line of force at p is along the line y = x 3 1
, where p is also a point lying on the same line then find
i2/i1

Answer 1

Given: Two mutually perpendicular infinite wires along x axis and y axis carry charge densities λ1 and λ2.

To find: Ratio of λ2 / λ1

Solution:

• Now we have given the straight line : y = x / √3

• Now comparing it with y = mx, we get:

                m = 1 / √3 = tan Ф

• Now let E2 be along x axis, then E2 will be:

                E2 = λ2 / 2π∈ox

• Let E1 be along y axis, then E1 will be:

                E1 = λ1 / 2π∈oy

• Now tanФ = y / x = E1 / E2         .................(i)

                E1 / E2  =  λ1 / 2π∈oy  /   λ2 / 2π∈ox

                E1 / E2  = λ1 x /  λ2 y

• Now x/y = √3    .............given

• So: E1 / E2  = √3 λ1 / λ2

• So from (i), we get:

               tan Ф = √3 λ1 / λ2

               1 / √3 = √3 λ1 / λ2

               λ1 / λ2 = 1/3

Answer:

          So the ratio of λ1 / λ2 is 1/3.