Doubling the point charge q while keeping distance r fixed changes the electric field magnitude by what factor?

Doubling the point charge q while keeping distance r fixed changes the electric field magnitude by what factor?

• A. It remains the same
• B. It doubles
• C. It quadruples
• D. It halves

Answer: (B)

The electric field magnitude from a point charge at a fixed distance r scales directly with the charge. For a point charge, E = k q / r^2. With r constant, k and r^2 are fixed, so E is proportional to q. If you double q to 2q, the field becomes E = k (2q) / r^2 = 2 (k q / r^2), which is twice the original. So the factor is two. The other options would require no change, a fourfold increase, or a decrease, which don’t happen when only the charge is increased while distance stays the same.

The electric field magnitude from a point charge at a fixed distance r scales directly with the charge. For a point charge, E = k q / r^2. With r constant, k and r^2 are fixed, so E is proportional to q. If you double q to 2q, the field becomes E = k (2q) / r^2 = 2 (k q / r^2), which is twice the original. So the factor is two. The other options would require no change, a fourfold increase, or a decrease, which don’t happen when only the charge is increased while distance stays the same.