If a dielectric of constant κ is inserted into a capacitor that is held at a fixed voltage, what happens to the electric field E and the charge Q?

• A. E decreases by a factor κ, and Q increases by κ
• B. E increases by a factor κ, and Q increases by κ
• C. E decreases by κ, and Q decreases by κ
• D. E increases by κ, and Q decreases by κ

Answer: (A)

With the capacitor held at a fixed voltage, the potential difference between the plates cannot change. The electric field between the plates is set by E = V/d, so the dielectric does not alter the field; it remains the same.

The dielectric does, however, increase the capacitor’s ability to store charge. The capacitance becomes C = κ C0, so to maintain the same voltage the source must supply more charge: Q = C V, which grows by a factor of κ.

In short: the electric field stays the same, while the charge increases by κ. If the charge were fixed instead, the field would drop by κ, illustrating the difference between fixed voltage and fixed charge scenarios.