Question

A small object has a charge of q = 2e, where e is the charge on an electron. 

(a) Determine the electric potential (in V) due to the charge at a distance r = 0.100 cm from the charge.

(b) Determine the electric potential difference in V) between a point that is 2r away and this point, that is V(2r) - V(r). 

(c) Determine the electric potential difference (in V) between a point that is r/2 away and this point, that is V(r/2) - V(r). 

(d) How would the answers change if the electrons are replaced by protons? 

• The sign of answer (a) would change. 

• The sign of answer (b) would change. 

• The sign of answer (c) would change. 

• The sign of all answers would change. 

• All answers would remain the same.

Answer 1

a)

electric potential is given as

V_r = k q/r

V_r = (9 x 10⁹)(2 x 1.6 x 10^-19)/(0.001)

V_r = 2.88 x 10^-6 volts

b)

electric potential is given as

V_2r = k q/(2r)

V_2r = (9 x 10⁹)(2 x 1.6 x 10^-19)/(2(0.001))

V_2r = 1.44 x 10^-6 volts

V_2r - V_r

(1.44 x 10^-6 ) - (2.88 x 10^-6)

- 1.44 x 10^-6

c)

electric potential is given as

V_r/2 = k q/(r/2)

V_r/2 = (9 x 10⁹)(2 x 1.6 x 10^-19)/((0.001)/2)

V_r/2 = 5.76 x 10^-6 volts

V_r/2 - V_r

(5.76 x 10^-6 ) - (2.88 x 10^-6 )

2.88 x 10^-6 volts