Four electric field vectors have been measured at the mid-points of the sides of a…

PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Electric Force Field and Potential · Electric Force Field and Potential

Problem

Four electric field vectors have been measured at the mid-points of the sides of a square of side 2 cm whose centre is at the origin of an

x

–

y

coordinate system. The measurements are as follows: • At

(0, +1\,\text{cm})

the field has magnitude

5\,\text{N/C}

and points toward the negative

x

-axis. • At

(0, -1\,\text{cm})

the field has magnitude

5\,\text{N/C}

and points toward the positive

x

-axis. • At

(+1\,\text{cm}, 0)

the field has magnitude

3\,\text{N/C}

and points toward the negative

y

-axis. • At

(-1\,\text{cm}, 0)

the field has magnitude

3\,\text{N/C}

and points toward the positive

y

-axis. (1) Part 1: (a) Using only the information given and assuming the field varies smoothly through space, determine an approximate value (magnitude and direction) for the electric field at the origin. Clearly articulate the steps in your reasoning. (2) Part 2: (b) Explain why the method you used in part (a) is expected to give a reasonable estimate, and discuss at least one limitation of the approximation.

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