An electric field of 1000 V/m is applied to an electric dipole at angle of $$45°$$. The value of electric dipole moment is $$10^{-29}$$ C.m. What is the potential energy of the electric dipole?

We start by recalling the expression for the potential energy of an electric dipole kept in a uniform electric field. The general formula is stated as $$U = -\vec p \cdot \vec E$$, where $$\vec p$$ is the electric dipole moment and $$\vec E$$ is the electric field.

Because the dot product of two vectors is the product of their magnitudes and the cosine of the angle between them, we can rewrite the formula as

$$U = -pE\cos\theta,$$

where
$$p$$ is the magnitude of the dipole moment,
$$E$$ is the magnitude of the electric field, and
$$\theta$$ is the angle between $$\vec p$$ and $$\vec E$$.

Now we substitute the numerical values given in the problem:

$$p = 10^{-29}\ \text{C·m}$$, $$\qquad E = 1000\ \text{V/m}$$, $$\qquad \theta = 45^\circ.$$

Placing these into the formula, we have

$$U = -(10^{-29})(1000)\cos 45^\circ.$$

First, multiply the magnitudes:

$$10^{-29} \times 1000 = 10^{-29}\times 10^{3} = 10^{-26}.$$

So the expression becomes

$$U = -10^{-26}\cos 45^\circ.$$

Next, we use the trigonometric value $$\cos 45^\circ = \dfrac{1}{\sqrt{2}} \approx 0.707.$$ Substituting this value, we get

$$U = -10^{-26} \times 0.707.$$

Performing the multiplication gives

$$U \approx -7.07 \times 10^{-27}\ \text{J}.$$

When we round to one significant figure, the result is

$$U \approx -7 \times 10^{-27}\ \text{J}.$$

This numerical value matches Option B in the given list.

Hence, the correct answer is Option B.