Work required to move the charge

[HelloMotto]

Homework Statement

a 2.0 pico C charge is locted at point A on an imaginary spherical surface which is centre on a 4.0 micro C point charge 2.8 cm away . How much work is required to move the 2.0 pico C charge to the following two points?

a) to point B, which is located on the same spherical surface an arc length of 3.0 cm away
b) to point C, which is located radially outward from A on another imaginary spherical surface of radius 4.2 cm.
c)what name could be used to describe these spherical surfaces?

Homework Equations

I have no Idea but since the question is looking for work, I am assuming this equation must be used
W= FDCosTheta
Electric force equation? FQ=K(q1q2/r^2)

 

[Redbelly98]

In your course, have they discussed electric potential or voltage yet? If so, that would be a "shortcut" to solving this problem.

If not then you'll have to use the equations for work and force to solve it.

 

[baba89]

To answer the first part of the question, we need to use the equation for electric potential energy, which is given by:
U = k(q1q2)/r
where k is the Coulomb's constant, q1 and q2 are the two charges, and r is the distance between them.

a) To move the 2.0 pico C charge from point A to point B, the distance traveled is 3.0 cm. Therefore, the work required is:
W = U(B) - U(A)
= k(q1q2)/r(B) - k(q1q2)/r(A)
= k(q1q2)(1/r(B) - 1/r(A))
= k(2.0x10^-12C)(4.0x10^-6C)(1/3.0x10^-2m - 1/2.8x10^-2m)
= 6.67x10^-11Nm^2/C^2(8.0x10^-18 - 7.14x10^-18)
= 0.53x10^-28J
Therefore, the work required to move the charge from point A to point B is 0.53x10^-28J.

b) To move the 2.0 pico C charge from point A to point C, the distance traveled is 4.2 cm. Therefore, the work required is:
W = U(C) - U(A)
= k(q1q2)/r(C) - k(q1q2)/r(A)
= k(q1q2)(1/r(C) - 1/r(A))
= k(2.0x10^-12C)(4.0x10^-6C)(1/4.2x10^-2m - 1/2.8x10^-2m)
= 6.67x10^-11Nm^2/C^2(7.14x10^-18 - 7.14x10^-18)
= 0J
Therefore, the work required to move the charge from point A to point C is 0J, as the potential energy at both points is the same.

c) The name that could be used to describe these spherical surfaces is equipotential surfaces, as they are imaginary surfaces where the electric potential is the same at all points on the surface.