Consider two point charges of equal magnitude but opposite sign placed symmetrically along the x-axis at positions $-a$ and $a$. At which point or points along the x-axis is the electric field zero?

• A. There is no point along the x-axis where the electric field is zero
• B. At a point outside the segment joining the charges, specifically at $x>a$ or $x<-a$
• C. At the midpoint between the two charges, $x=0$
• D. At both $x=a$ and $x=-a$

Answer: (B)

Verified step by step guidance

1. Identify the positions and magnitudes of the two point charges: one positive charge +q at x = +a and one negative charge -q at x = -a along the x-axis.
2. Recall that the electric field due to a point charge q at a distance r is given by \(E = \frac{1}{4\pi\epsilon_0} \frac{q}{r^2}\), directed away from the charge if q is positive and toward the charge if q is negative.
3. Set up the expression for the net electric field at a general point x on the x-axis by summing the contributions from both charges, taking care to consider the direction (sign) of each field vector.
4. Write the equation for the net electric field being zero: \(E_{net} = E_{+q} + E_{-q} = 0\), and solve for x. This will involve equating the magnitudes of the fields and considering their directions.
5. Analyze the solutions to determine where along the x-axis the electric field cancels out. Note that the field cannot be zero between the charges because the fields from opposite charges add up there, but it can be zero at points outside the segment joining the charges, specifically for \(x > a\) or \(x < -a\).