Question

an electric dipole of dipole moment P is placed in a uniform electrostatic field E for what angle between P & E the potential energy be half of max value​

Answer 1

Using the formula,

Electrostatic Potential energy of the dipole placed in an uniform electric field is given by the formula,

U = PESinθ,

where θ is the angular displacement of dipole.

Don't think the formula of torque here, both are same but the meaning of angle in both case is different.]

Now, U = PESinθ will be max., when Sinθ = 1,

Thus, Umax. = PE

Now, As per as question, U = 1/2 U max.

U = PE/2

PESinθ = PE/2

Sinθ = 1/2

Sinθ = Sin(π/6)

when Sinθ = Sinα, then,

θ = πn + (-1)ⁿα

Thus, θ = π/6, 5π/6, etc.

Hope it helps.

Answer 2

torque will be maximum is 90°