AcademyElectric Charge and Fields
Academy
Charge Induction
Level 1 - Physics topic page in Electric Charge and Fields.
Principle
Charge induction uses an external electric field to separate charge, and grounding can turn that separation into a net charge.
Notation
\(Q_{\mathrm{obj}}\)
net charge of the object
\(\mathrm{C}\)
\(Q_{\mathrm{near}}\)
charge shifted toward an external charged body
\(\mathrm{C}\)
\(Q_{\mathrm{far}}\)
charge shifted away from an external charged body
\(\mathrm{C}\)
\(\vec E_{\mathrm{ext}}\)
external electric field
\(\mathrm{N\,C^{-1}}\)
\(\Delta Q_{\mathrm{ground}}\)
charge transferred through a ground connection
\(\mathrm{C}\)
Method
Derivation 1: Separate charge without changing net charge
Bring a charged body near a neutral conductor. Free charges in the conductor move in response, but if the conductor is isolated, its total charge remains zero.
Neutral start
\[Q_{\mathrm{obj}}=0\]
Separation
\[Q_{\mathrm{near}}+Q_{\mathrm{far}}=0\]
No contact
\[\Delta Q_{\mathrm{obj}}=0\]
The charge has redistributed, not entered or left the object.
Derivation 2: Use grounding to change net charge
A ground connection allows charge to cross the object boundary. The sign left behind is determined by which sign is repelled or attracted by the external charged body.
Ground transfer
\[Q_{\mathrm{obj,final}}=-\Delta Q_{\mathrm{ground}}\]
Positive external body
\[e^-\ \text{is attracted from ground to object}\]
Final sign
\[Q_{\mathrm{obj}}<0\quad\text{after ground is removed}\]
Rules
These rules separate redistribution from charging.
Isolated induction
\[\Delta Q_{\mathrm{obj}}=0\]
Separated neutral charges
\[Q_{\mathrm{near}}=-Q_{\mathrm{far}}\]
Grounding changes charge
\[\Delta Q_{\mathrm{obj}}\ne0\quad\text{only while a conducting path is present}\]
Opposite final sign
\[\text{charging by induction leaves sign opposite the nearby external charge}\]
Examples
Question
A negative rod is brought near an isolated neutral metal sphere. Which side of the sphere becomes positive?
Answer
Electrons in the sphere are repelled by the negative rod, so the side nearer the rod is electron-deficient and becomes positive.
Checks
- Induced separation in an isolated neutral conductor does not change its net charge.
- Grounding matters only while the connection exists.
- Remove the ground before removing the external charged body when charging by induction.
- The final induced net charge has the sign opposite the external body used during grounding.