Question

The electric potential in a region that is within 2. 00 m of the origin of a rectangular coordinate system is given by V=Axl+Bym+Czn+D, where A, B, C, D, l, m, and n are constants. The units of A, B, C, and D are such that if x, y, and z are in meters, then V is in volts. You measure V and each component of the electric field at four points and obtain these results:Point (x,y,z)(m) V(V) Ex(V/m) Ey(V/m) Ez(V/m) 1 (0, 0, 0) 10. 0 0 0 0 2 (1. 00, 0, 0) 4. 0 16. 0 0 0 3 (0, 1. 00, 0) 6. 0 0 16. 0 0 4 (0, 0, 1. 00) 8. 0 0 0 16. 0

Use the data in the table to calculate A.

Use the data in the table to calculate B

Use the data in the table to calculate C

Use the data in the table to calculate D

Use the data in the table to calculate E

Use the data in the table to calculate l

Use the data in the table to calculate m

Use the data in the table to calculate n

Answer 1

A, B, C, D, l, m, and n are constants in the equation V=Axl+Bym+Czn+D, so we can use the data in the table to calculate their values.

To calculate A, we can use the point (1.00, 0, 0) and the equation V=Axl+Bym+Czn+D. Substituting the values into the equation, we get: 4.0 = A(1.00) + B(0) + C(0) + D.

To calculate B, we can use the point (0, 1.00, 0) and the equation V=Axl+Bym+Czn+D. Substituting the values into the equation, we get: 6.0 = A(0) + B(1.00) + C(0) + D.

To calculate C, we can use the point (0, 0, 1.00) and the equation V=Axl+Bym+Czn+D. Substituting the values into the equation, we get: 8.0 = A(0) + B(0) + C(1.00) + D.

To calculate D, we can use the point (0, 0, 0) and the equation V=Axl+Bym+Czn+D. Substituting the values into the equation, we get: 10.0 = A(0) + B(0) + C(0) + D.

The values of Ex, Ey, and Ez are not related to the calculation of A, B, C and D.

To calculate l, m, and n we can use the values of Ex, Ey, and Ez.

Ex = A, Ey = B, and Ez = C

We can use the values of Ex, Ey, and Ez at the points (1.00, 0, 0), (0, 1.00, 0), and (0, 0, 1.00) respectively.