A rectangular grid with points spaced 2 cm apart extends through the region and

PHYSICS · Multi-part · GCSE · Physics · Electricity · Electricity

Problem

A rectangular grid with points spaced 2 cm apart extends through the region

-4\,\text{cm}\le x\le +4\,\text{cm}

and

-4\,\text{cm}\le y\le +4\,\text{cm}

. Electric field vectors have been measured only along the vertical line

x=0\,\text{cm}

and the parallel line

x=+4\,\text{cm}

: • For every point on

x=0\,\text{cm}

between

y=-4\,\text{cm}

and

y=+4\,\text{cm}

, the field is

12\,\text{N/C}

pointing straight upward. • For every point on

x=+4\,\text{cm}

in the same

y

interval, the field is

6\,\text{N/C}

pointing straight upward. No other vectors are given. (a) Determine an approximate value (magnitude and direction) for the electric field at the grid point

(2\,\text{cm},0\,\text{cm})

. Show all reasoning that leads to your estimate. (b) On your own coordinate grid, sketch electric field vectors at the points

(2\,\text{cm},+2\,\text{cm})

and

(2\,\text{cm},-2\,\text{cm})

that are consistent with the overall pattern revealed by the original data. Explain how you decided on both the directions and the relative lengths of these new arrows. (c) Translate your completed vector map into an electric-field-line diagram covering the entire rectangular region. In words, describe how the spacing of the field lines varies across the region and how that spacing communicates information about field strength. (d) A new point charge is now placed at the grid point

(2\,\text{cm},0\,\text{cm})

. Near that point, its own field would create arrows of

4\,\text{N/C}

pointing straight downward. Describe qualitatively how the vector map and the field-line diagram you produced in parts (b) and (c) would adjust once this charge is introduced.

Related theory

Browse the problem library