Consider two point charges of equal magnitude but opposite sign placed a distance $d$ apart along the x-axis, as shown in Figure 1(a). At which point or points along the line joining the charges is the electric field zero?

• A. At a point closer to the negative charge
• B. At a point closer to the positive charge
• C. At a point exactly midway between the two charges
• D. There is no point along the line joining the charges where the electric field is zero

Answer: (C)

Verified step by step guidance

1. Identify the positions of the two point charges: let the positive charge +q be at position x = 0 and the negative charge -q be at position x = d along the x-axis.
2. Recall that the electric field due to a point charge q at a distance r is given by \(E = \frac{k|q|}{r^2}\), where \(k\) is Coulomb's constant, and the direction depends on the sign of the charge.
3. Set up the expression for the net electric field at a general point x along the x-axis between and outside the charges. Consider the contributions from both charges and their directions.
4. Analyze the net electric field at different regions: to the left of the positive charge (x < 0), between the charges (0 < x < d), and to the right of the negative charge (x > d), to find where the fields can cancel each other out.
5. Conclude that the electric field cannot be zero at the midpoint or between the charges because the fields from opposite charges add up in the same direction there; instead, the zero field point lies outside the segment, closer to the charge with smaller magnitude or depending on the sign, so verify this by solving the equation \(E_{net} = 0\) for x.