Two point charges (+q) and (−2q) are fixed on the x-axis at positions a and 2a from origin respectively. At what positions on the axis, the resultant electric field is zero
Answers
let the electric field be zero at a position x from the origin
1= particle +q
2=particle -2q
we know that electric field can be zero only at one place ie on the left of particle +q
E1=kq/(a-x)²
E2=k(-2q)/(2a-x)²
E1+E2=0
E1=-E2
kq/(a-x)²=2qk/(2a-x)²
1/a-x=√2/(2a-x)
2a-x=√2(a-x)
2a-√2a=-√2x+x
√2a(√2-1)=-x(√2-1)
x=-√2a
therefore its at a distance of √2a on the left side of number line.
Answer:let the electric field be zero at a position x from the origin
1= particle +q
2=particle -2q
we know that electric field can be zero only at one place ie on the left of particle +q
E1=kq/(a-x)²
E2=k(-2q)/(2a-x)²
E1+E2=0
E1=-E2
kq/(a-x)²=2qk/(2a-x)²
1/a-x=√2/(2a-x)
2a-x=√2(a-x)
2a-√2a=-√2x+x
√2a(√2-1)=-x(√2-1)
x=-√2a
therefore its at a distance of √2a on the left side of number line.
:)