Question

An electric field has SI units of N C⁻¹. Express the dimensional relationship between force (F), charge (q₀), and the electric field (E).

Options

• \[\vec{E} = \frac{\vec{F}}{q_0}\], which shows force equals electric field times charge

• \[\vec{E} = \vec{F} \times q_0\], which shows field equals force times charge

• \[\vec{F} = \frac{\vec{E}}{q_0}\], which shows charge equals force divided by field

• \[q_0 = \vec{F} \times \vec{E}\], which shows charge equals force times field

Answer 1

The definition of electric field is \[\vec{E} = \frac{\vec{F}}{q_0}\], which can be rearranged to \[\vec{F} = q_0\vec{E}\]. This relationship shows that the force on a test charge is the product of the charge and the electric field at that location. The SI units confirm this: if E is in N C⁻¹ and q₀ is in C (Coulombs), then F = q₀E is in (C)(N C⁻¹) = N (Newtons), which is correct for force.