The correct option is B 120∘
Let phase difference Δϕ=ϕ1−ϕ2
We know resultant amplitude is,
Ar=√A21+A22+2A1A2cosΔϕ
Given: Ar=A, substituting it in above formula gives
⇒A=√A2+A2+2A2cosΔϕ
⇒A=√2A2(1+cos Δϕ)
⇒1√2=√1+cos Δϕ
Squaring both sides,
⇒1+cos Δϕ=12
cos Δϕ=−12
The negative value of cosΔϕ indicates that it must be an angle of either second or third quadrant.
⇒Δϕ=π−π3=2π3or Δϕ=π+π3=4π3
∴Δϕ=2π3=120∘, is the correct answer.