A square grid of points in the –plane is spaced by in each direction
PHYSICS · Multi-part · CBSE · Physics · Electrostatic Potential and Capacitance · Electrostatic Potential and Capacitance
Problem
A square grid of points in the xy–plane is spaced by 1.0cm in each direction. The table lists the electric potential (in volts) measured at five specific grid points surrounding the origin.
Point
(x,y) in cm
V (V)
P
(−1,+1)
14
Q
(+1,+1)
10
R
(−1,−1)
18
S
(+1,−1)
12
O
(0,0)
15
Assume the potential varies smoothly between the listed points.
(a) Using the information in the table, estimate the x–component and the y–component of the electric field at the origin O. Show all steps in your reasoning.
(b) Calculate the magnitude of the electric field at O from the components obtained in part (a), and state its direction as an angle measured counter-clockwise from the +x–axis.
(c) On a set of coordinate axes you create, sketch at least three electric field lines in the vicinity of the origin that are consistent with the potential data provided. Clearly label the orientation of each line.
(d) Explain qualitatively why the spacing of your field lines near the origin is or is not uniform, making explicit reference to the numerical results from parts (a) and (b).