A cross-section of equipotential surfaces is shown. The lines contain the given

Question

A cross-section of equipotential surfaces is shown. The lines contain the given points along with their electric potentials are as follows: a (90 volts), b (40 volts), c & d (-20 volts). Determine/calculate the following: a) The magnitude of the Electric Field along the regions be where distance be is 2 cm. b) The work (in eV) required to move a proton from point d to a: c) The work (in eV) required to move an electron from point b to d: d) The work (in eV) required to move an electron from point c to d:

Explanation / Answer

Given Va = 90 Volt, Vb = 40Volt, Vc = -20 Volt and Vd = -20 Volt

a) There is a relation between electric field and change in potential

E = -dV/dr

Here for bc regions

|E| = [40-(-20)]/0.02 = 3000 N/C

b) Work done by electric field = change in potential energy = qp (Vd-Va)

                                     = 1e *(-20 -90) = -110 eV

So work done by an external agent = -( Work done by electric field) = 110 eV

c) Work done by electric field = change in potential energy = qe (Vb-Vd)

                                     = -1e *(40-(-20)) = -60eV

So work done by an external agent = -( Work done by electric field) = 60 eV

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