Question

A 1mc charge is separated from a 3mc charge by 10m. If the P denotes the point of Zero electric field between the charges, determine the distance x, from the 1mc chrage?

a) 3.71m
b) 3.66m
c)3.12m
d)4.36m

Answer 1

Given Data,

Q₁ = 1mC = 0.001 C

Q₂ = 3 mC = 0.003 C

Distance (D)= 10m

Find the point(P) where zero electric field between the charges.

Sol:

Let's say the point is P which is X m distance from charge Q₁ and (D-X) m distance from Q₂. As Q₂>Q₁ so the point must be closer to the weak charge i.e Q₁ .

As we know, the electric field of one point charge q from a distance r is denoted by, E = k (q/r²).

so, E₁ = k (Q₁/X²)

And, E₂ = k (Q₂/ (D-X)²)

At point P, E₁ = E₂ to cancel each other and become zero electric field,

E₁ = E₂

_Or, k (Q₁/X²) = k (Q₂/ (D-X)²)

Or, 1/X² = 3/(10-X)²

Or, 1/X = 1.732/(10-X)           [taking root both sides]

Or, 1.732X = 10 - X

Or, 1.732X + X = 10

Or, 2.732 X = 10

Or, X = 10/2.732

Or, X = 3.66

So, the the P denotes the point of Zero electric field between the charges, the distance 3.66m, from the 1mc charge .

So, the correct option is (b)