Question

A POSITIVE POINT CHARGE q1 creates an electric field of magnitude E1 at a spot located at a distance r1 from the charge. The charge is replaced by another positive point charge q2, which creates a field of magnitude E2=E1 at a distance of r2=2r1. How is q2 related to q1? (a)q2=2q1 (b)q2=1/2q1 (c) q2= 4q1 (d)q2 =1/4 q1 (e) q2= sqroot 2 q1

Answer 1

Answer:

 q₂ = 4 q₁

Explanation:

We know ,electric fled due to a charge q is given as

$E=K\dfrac{q}{r^2}$

q=Charge

r=Distance

K=Constant

E=Electric field

Electric field due to charge q₁

$E_1=K\dfrac{q_1}{r_1^2}$      

Electric field due to charge q₂

$E_2=K\dfrac{q_2}{r_2^2}$

E₂ = E₁

r₂ = 2 r₁      

$K\dfrac{q_2}{r_2^2}=K\dfrac{q_1}{r_1^2}$

$\dfrac{q_2}{(2r_1)^2}=\dfrac{q_1}{r_1^2}$

$\dfrac{q_2}{4r_1^2}=\dfrac{q_1}{r_1^2}$

q₂ = 4 q₁

Therefore the option C is correct.