test charge

Meaning: A test charge is a hypothetical point charge, by convention positive, placed at a location to find the electric field or potential there. It is taken to be small enough that it does not shift the source charges that create the field. Because it is positive, the field points away from positive sources and toward negative sources.

Equation: E = F/q₀, where E is the electric field (N/C, equal to V/m), F is the electric force on the test charge (N), and q₀ is the test charge (C). For a point source Q at distance r, E = kQ/r², where k = 8.99 × 10⁹ N·m²/C² and r is in m.

On the MCAT: Passages draw several source charges and ask which way a test charge would accelerate, or where the net field is zero. Field-line and equipotential diagrams are common. You may also be asked about the work needed to move a test charge between two points. An external agent moving it at constant speed does work W = q₀ΔV, where V is potential (volts) and W is in joules. A test charge released from rest moves toward lower potential energy.

Common confusion: Students think the field depends on the test charge. It does not. Doubling q₀ doubles the force, but E at that point stays the same, because E belongs to the source charges. If the test charge is negative, the force is opposite to the field direction, although the field itself is unchanged.