In the image method for a point charge q located at distance d from an infinite grounded conducting plane, the image charge has what magnitude and sign, and where is it located?

In the image method for a point charge q located at distance d from an infinite grounded conducting plane, the image charge has what magnitude and sign, and where is it located?

• A. Magnitude q, same sign, located at distance d.
• B. Magnitude q, opposite sign, located at distance -d along the axis.
• C. Magnitude 2q, opposite sign, located at -d.
• D. Magnitude q, opposite sign, located at 2d.

Answer: (B)

The key idea is the image method: to satisfy the grounded plane boundary, replace the plane by an image charge arranged so the potential vanishes on the plane. For a real charge q at distance d from the plane, placing an image charge of equal magnitude but opposite sign at the mirror point on the other side (the same distance d from the plane) makes the potential on the plane cancel out. In other words, the image has magnitude q, opposite sign, located at the mirror position distance d on the opposite side of the plane (often described as along the same axis but at -d). This setup also means the two charges are 2d apart, producing the familiar attractive interaction that the image method mirrors.

The key idea is the image method: to satisfy the grounded plane boundary, replace the plane by an image charge arranged so the potential vanishes on the plane. For a real charge q at distance d from the plane, placing an image charge of equal magnitude but opposite sign at the mirror point on the other side (the same distance d from the plane) makes the potential on the plane cancel out. In other words, the image has magnitude q, opposite sign, located at the mirror position distance d on the opposite side of the plane (often described as along the same axis but at -d). This setup also means the two charges are 2d apart, producing the familiar attractive interaction that the image method mirrors.