Compared to the electric field energy density at b, the electric field energy density at a is large by a factor of 16.
<h3>What is potential energy?</h3>
The energy of a particle by virtue of its position.
The potential at B = Vb =V
Vb = 1/4π∈₀ x e/r₁ = ke/r₁
V =ke/r₁
and r₁ = ke /V
The potential at A = Va = 2V
2V = ke/r₂
r₂ = ke/2V
The electric field at point B. Eb = ke/r₁²
Substitute the value of r₁, we get
Eb = V²/ke
The electric field at point A , Ea = ke /r₂²
Substitute the value of r₂, we get
Ea = 4V²/ke
The electric field energy density at point A and B,
Ua = 1/2 ∈Ea²
Ub = 1/2 ∈Eb²
electric field energy density is proportional to the square of electric field at the particular point.
Ua/Ub =(Ea/Eb)²
Substitute the values, we get
Ua/Ub = 16
Thus, compared to the electric field energy density at b, the electric field energy density at a is large by a factor of 16.
Learn more about potential energy.
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