Question

A charge of 5C is placed at the origin and -10C is placed at thed point x=30. Find a point on the x axis at which electric firld is zero.​

Answer 1

Answer:

the points at X axis where electric field is zero are (-10 , 0) and (30,0)

Explanation:

Data:

charge = Q1= 5 C

charge = Q2= -10 C

Distance between charges on line= r = 30

electric field due to Q1 = E1

electric field due to Q1 = E2

Required :

point at which electric field = 0

Calculation:

let "x" be a point at which electric field is zero and

let

distance of Q1 from point "x" = d

distance of Q1 from point "x" = d - 30

Then

It is possible only whence electric field produce by both charges is equal that is

  E1 = E2   .....(1)

We know that

  E1 = k Q1 / (d^2)   .....(2)

And

  E2 = k Q2 / (d - 30)^2)   ......(3)

Putting the values of E1 and E2 in equation (1) we get

  k Q1 / (d^2) =  k Q2 / ((d -30)^2)

⇒ Q1 / (d^2) =  Q2 / (( d - 30)^2)

⇒ Q1  ( d - 30)^2)  =  Q2 (d^2)

Putting the values of Q1 and Q2 we get

   5 ((30-d)^2) = (-10)(d^2)

⇒    ((30-d)^2) = (-2)(d^2)                  

⇒       900+d^2-60d = -2(d^2)

⇒       3d^2 -60d + 900 = 0

⇒          d^2 -20d + 300 = 0

By factorization we get

       (d-30)(d+10) = 0

⇒       d = 30   or d = -10

because Q1 is at origin therefore

when d=30 then x = 30

and

when d = -10 then x = -10

So the points at X axis where electric field is zero are (-10 , 0) and (30,0)