Question

A proton and an electron are fixed in space with a separation of 859 nm. Calculate the electric potential at the midpoint between the two particles.

Answer 1

Answer:

The electric potential at the midpoint between the two particles is 3.349 X 10⁻³ Volts

Explanation:

Electric potential is given as;

V = E*r

where;

E is the electric field strength, = kq/r²

V = ( kq/r²)*r

V = kq/r

k is coulomb's constant = 8.99 X 10⁹ Nm²/C²

q is the charge of the particles = 1.6 X 10⁻¹⁹ C

r is the distance between the particles = 859 nm

At midpoint, the distance = r/2 = 859nm/2 = 429.5 nm

V = (8.99 X 10⁹  * 1.6 X 10⁻¹⁹)/ (429.5 X 10⁻⁹)

V = 3.349 X 10⁻³ Volts

Therefore, the electric potential at the midpoint between the two particles is 3.349 X 10⁻³ Volts

Answer 2

The electric potential between the two particles is zero

To calculate the electric potential between the two point, we have to take into cognizance that we are finding the potential at mid-points.

Data given;

• x = 859nm
• at mid point, x= x/2 = 429.5*10^-9m
• k = 9*10^9
• e = 1.6*10^-19J

The Electric potential

This is given by the formula

$v = \frac{Ke}{x}$

But since we are calculating for the potential at midpoint,

$v = \frac{ke}{x/2} - \frac{ke}{x/2}$

Substituting the values into the equation above and solve

$v = \frac{9*10^9*1.6*10^-^1^9}{429.5*10^-^9}-\frac{9*10^9*1.6*10^-^1^9}{429.5*10^-^9}\\ v = 0$

The electric potential at the midpoint between the two particles is 0.

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