23.79 - DATA The electric potential in a region that is within 2.00 m of the origin of a rectangular coordinate system is given by V = Ax' + By" + C2" + D, where A, B, C, D, I, m, and n are constants. The units of A, B, C, andD are such that if x, y, and z are in meters, then V is in volts. You measure V and each com- ponent of the electric field at four points and obtain these results: Point (x,y,z) (m) v(v) E.(V/m) E, (V/m) E; (V/m) v (V) (0, 0, 0) 10.0 2 (1.00, 0, 0) 4.0 12.0 3 (0, 1.00, 0) 6.0 12.0 4 (0, 0, 1.00) 8.0 12.0 (a) Use the data in the table to calculate A, B, C, D, I, m, and n. (b) What are V and the magnitude of E at the points (0, 0, 0), (0.50 m, 0.50 m, 0.50 m), and (1.00 m, 1.00 m, 1.00 m)?

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23.79 * DATA The electric potential in a region that is within
2.00 m of the origin of a rectangular coordinate system is given
by V = Ar' + By" + Cz" + D, where A, B, C, D, 1, 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 com-
ponent of the electric field at four points and obtain these results:
Point (r, y, 2) (m) v(V) E, (V/m) E, (V/m) E, (V/m)
(0, 0, 0)
10.0
(1.00, 0, 0)
4.0
12.0
3
(0, 1.00, 0)
6.0
12.0
4
(0, 0, 1.00)
8.0
12.0
(a) Use the data in the table to calculate A, B, C, D, 1, m, and n.
(b) What are V and the magnitude of E at the points (0, 0,0),
(0.50 m, 0.50 m, 0.50 m), and (1.00 m, 1.00 m, 1.00 m) ?
2.
Transcribed Image Text:23.79 * DATA The electric potential in a region that is within 2.00 m of the origin of a rectangular coordinate system is given by V = Ar' + By" + Cz" + D, where A, B, C, D, 1, 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 com- ponent of the electric field at four points and obtain these results: Point (r, y, 2) (m) v(V) E, (V/m) E, (V/m) E, (V/m) (0, 0, 0) 10.0 (1.00, 0, 0) 4.0 12.0 3 (0, 1.00, 0) 6.0 12.0 4 (0, 0, 1.00) 8.0 12.0 (a) Use the data in the table to calculate A, B, C, D, 1, m, and n. (b) What are V and the magnitude of E at the points (0, 0,0), (0.50 m, 0.50 m, 0.50 m), and (1.00 m, 1.00 m, 1.00 m) ? 2.
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