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A point charge Q is located at (r, y, z) quadrant r > 0, y > 0 is bounded by two grounded conducting planes defined separately by y = 0 and r = 0. Solve for V(r > 0, y > 0, z) using the method of image charges. (a) The potential (x > 0,y > 0, z) can be obtained by in- cluding image charges qa (x, y, z) = (-a, b,0), q at (a, -b, 0) and qab at (-a, -b, 0). Demonstrate by explicit calcula- tion of V(r, y, z) that the boundary conditions V (0, y > 0, z) = 0 and V(r > 0,0, z) = 0 are satisfied if q. = q6 = -Q and qab = +Q = (a, b, 0), as shown in the drawing. The %3D in the physical region at coordinates y vx x plane (a,b) (a,b) %3D %3D (-a,-b) (a,-b) (b) What is the surface charge density on the grounded plane at (x, y, z) = (a, 0,0)?

A point charge Q is located at (r, y, z) quadrant r > 0, y > 0 is bounded by two grounded conducting planes defined separately by y = 0 and r = 0. Solve for V(r > 0, y > 0, z) using the method of image charges. (a) The potential (x > 0,y > 0, z) can be obtained by in- cluding image charges qa (x, y, z) = (-a, b,0), q at (a, -b, 0) and qab at (-a, -b, 0). Demonstrate by explicit calcula- tion of V(r, y, z) that the boundary conditions V (0, y > 0, z) = 0 and V(r > 0,0, z) = 0 are satisfied if q. = q6 = -Q and qab = +Q = (a, b, 0), as shown in the drawing. The %3D in the physical region at coordinates y vx x plane (a,b) (a,b) %3D %3D (-a,-b) (a,-b) (b) What is the surface charge density on the grounded plane at (x, y, z) = (a, 0,0)?

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A point charge Q is located at (x, y, z) quadrant r > 0, y > 0 is bounded by two grounded conducting planes defined separately by y = 0 and x = 0. Solve for V(x > 0, y 2 0, z) using the method of image charges. (a) The (x > 0, y > 0, z) can be obtained by in- cluding image charges qa (x, y, z) = at (-a, -b, 0). Demonstrate by explicit calcula- tion of V(r, y, z) that the boundary conditions V (0, y > 0, 2) = 0 and V(x > 0,0, z) = 0 are satisfied if qa = q6 = -Q and qab = +Q (a, b, 0), as shown in the drawing. The %3D %3D potential in the physical region at coordinates y vx x plane (-a, b, 0), qb at (a, -b, 0) and qab (a,b) (a,b) (-a,-b) (a,-b) (b) What is the surface charge density on the grounded plane at (x, y, z) = (a, 0, 0)?
Transcribed Image Text:A point charge Q is located at (x, y, z) quadrant r > 0, y > 0 is bounded by two grounded conducting planes defined separately by y = 0 and x = 0. Solve for V(x > 0, y 2 0, z) using the method of image charges. (a) The (x > 0, y > 0, z) can be obtained by in- cluding image charges qa (x, y, z) = at (-a, -b, 0). Demonstrate by explicit calcula- tion of V(r, y, z) that the boundary conditions V (0, y > 0, 2) = 0 and V(x > 0,0, z) = 0 are satisfied if qa = q6 = -Q and qab = +Q (a, b, 0), as shown in the drawing. The %3D %3D potential in the physical region at coordinates y vx x plane (-a, b, 0), qb at (a, -b, 0) and qab (a,b) (a,b) (-a,-b) (a,-b) (b) What is the surface charge density on the grounded plane at (x, y, z) = (a, 0, 0)?
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