A survey of the electrostatic potential in a region of the -plane produces a contour…

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Electricity, Magnetism & Electromagnetism · Electrostatic fields and potential

Electricity, Magnetism and Electromagnetism, Ch Electrostatic potential, potential energy and the energy of the field

Problem

A survey of the electrostatic potential in a region of the

xy

-plane produces a contour map: equipotential curves are drawn every

20\,\mathrm{V}

. All the charges that make the field are at rest, and

V

does not vary with

z

. Near a point

P

the perpendicular distance between the neighbouring equipotential curves labelled

60\,\mathrm{V}

and

80\,\mathrm{V}

4.0\,\mathrm{mm}

. Near a point

Q

, elsewhere on the same map, the perpendicular distance between the curves labelled

60\,\mathrm{V}

and

80\,\mathrm{V}

12.5\,\mathrm{mm}

. Over distances as small as these the field may be treated as uniform. ((a)) Find the magnitude of the electric field at

P

and at

Q

. ((b)) State the direction of the field at

P

relative to the equipotential curve through

P

, and say why the field must have that direction. ((c)) If field lines were drawn on the same map, would they be more closely spaced near

P

or near

Q

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