(a) The electric potential due to a point charge is given by V = kq⁄r where q is the charge, r is the distance from q and k = 8.99 × 109 m2 C 2 ⁄ . Show, in detail, that the SI unit of electric potential is a volt. ( b ) What are the equipotential lines? (c) How are equipotential lines used to obtain the electric field lines? (

(a) The unit of electric potential is volts.

(b) Equipotential lines are lines along which the electric potential is constant.

(c) Equipotential lines are obtained by drawing a line perpendicular to electric field lines.

Electric potential is the work done in moving a unit positive from infinite to a point in the electric filed.

Electric potential = EQ

Electric potential = (V/C) x (C)

Electric potential = Volts.

This is a line along which the electric potential is constant.

Equipotential lines are obtained by drawing a line perpendicular to electric field lines.

Learn more about equipotential lines here: link

a)  [volts] = [N m / C],

b) The lines or surface that has the same potential are called equipotential

c) the equipotential lines must also be perpendicular to the electric field lines

Explanation:

a) find the units of the volt

the electric potential energy is

             V = k q / r

             V = [N m² / C²] C / m

              V = [N m / C]

The electric potential is defined as

             V = E .s

             V = [N / C] [m]

             V = [N m / C] = [volt]

we see that in the two expressions the same result is obtained therefore the volt is

            [volts] = [N m / C]

b) The lines or surface that has the same potential are called equipotential surfaces, the great utility of these lines or surfaces is that a face can be displaced on it without doing work.

c) The electric potential is defined as the gradient of the electric field

             v =  

therefore the equipotential lines must also be perpendicular to the electric field lines

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