The electric potential energy between two positively charged particles is given by the equation:
U = k * (q1 * q2) / r
where U is the electric potential energy, k is Coulomb's constant, q1 and q2 are the charges of the particles, and r is the distance between them.
To increase the electric potential energy between two positively charged particles by a factor of 16, we can rearrange the above equation as follows:
U' = 16U
k * (q1 * q2) / r' = 16 * (k * (q1 * q2) / r)
where U' and r' are the new potential energy and distance, respectively.
Simplifying the above equation, we get:
r' = (1/4) * r
Therefore, the distance between the positively charged particles must be reduced by a factor of 4.
So, the correct option is:
B. Reduce the distance by a factor of 4.