Short Answer 
The potential energy (U) of an electric dipole in a uniform electric field is calculated using the formula U = -pE. Given the electric dipole moment (p) of 6.7 * 10^-10 C-m and electric field strength (E) of 10^4 N/C, the resulting potential energy is U = -6.968 * 10^-8 C-m/N.
Step 1: Understand the Formula
To determine the potential energy (U) of an electric dipole in a uniform electric field, we apply the formula U = -pE. In this equation:
- U refers to the potential energy of the dipole.
- p represents the electric dipole moment.
- E is the strength of the electric field.
Step 2: Insert Given Values
In our case, we have the following values for electric dipole moment and electric field strength:
- Electric dipole moment (p) = 6.7 * 10-10 C-m
- Electric field strength (E) = 104 N/C
Now, we can substitute these values into the formula: U = – (6.7 * 10-10) * (104).
Step 3: Perform the Calculation
To find the potential energy, calculate the product of the values:
- Multiply 6.7 by 10,000 (104): U = – (6.7 * 10,000 * 10-10) C-m/N.
- This simplifies to U = – 69680 * 10-10 C-m/N.
- Finally, simplify to express in standard notation: U = – 6.968 * 10-8 C-m/N.