Two point charges, with charges q and -2q are situated above a grounded conducting plane, as shown. a) What is the dipole moment, p, of this configuration (including any contribution from the grounded conducting plane)? b) What is the surface charge density, o(r), induced on this grounded plane by these charges? -29 e I d

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### Problem Description

Two point charges, with charges \( q \) and \( -2q \), are situated above a grounded conducting plane, as shown in the accompanying diagram.

#### Questions:
a) What is the dipole moment, \( \vec{p} \), of this configuration (including any contribution from the grounded conducting plane)?

b) What is the surface charge density, \( \sigma(r) \), induced on this grounded plane by these charges?

### Diagram Explanation

The diagram illustrates two point charges positioned vertically above a horizontal line representing a grounded conducting plane. The charge \( q \) is at a distance \( d \) above the plane, and the charge \( -2q \) is at a distance \( 2d \) from the conducting plane. 

The grounded plane implies that the electric potential on the plane's surface is zero, affecting how the charges above induce surface charges. The interaction between these point charges and the induced surface charges alters the electric field distribution around the plane.
Transcribed Image Text:### Problem Description Two point charges, with charges \( q \) and \( -2q \), are situated above a grounded conducting plane, as shown in the accompanying diagram. #### Questions: a) What is the dipole moment, \( \vec{p} \), of this configuration (including any contribution from the grounded conducting plane)? b) What is the surface charge density, \( \sigma(r) \), induced on this grounded plane by these charges? ### Diagram Explanation The diagram illustrates two point charges positioned vertically above a horizontal line representing a grounded conducting plane. The charge \( q \) is at a distance \( d \) above the plane, and the charge \( -2q \) is at a distance \( 2d \) from the conducting plane. The grounded plane implies that the electric potential on the plane's surface is zero, affecting how the charges above induce surface charges. The interaction between these point charges and the induced surface charges alters the electric field distribution around the plane.
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