Electric potential of tiny spheres question

In summary, two tiny metal spheres A and B with masses of 3.40 g and 3.90 g and charges of 4.50 µC are connected by a nonconducting string of length 1.00 m. The electric potential energy of the system is 0.18225 J. Upon cutting the string, the spheres experience accelerations of __m/s2 (Sphere A) and __m/s2 (Sphere B). After a long time has passed, the spheres will have speeds of __m/s (Sphere A) and __m/s (Sphere B). To solve for these values, conservation of energy and momentum are used.
  • #1
lodovico
17
0

Homework Statement


Two tiny metal spheres A and B of mass mA = 3.40 g and mB = 3.90 g have equal positive charges q = 4.50 µC. The spheres are connected by a massless nonconducting string of length d = 1.00 m, a distance that is much greater than the radii of the spheres.
(a) What is the electric potential energy of the system?
__J
(b) Suppose you cut the string. At that instant, what is the magnitude of the acceleration of each sphere?
__m/s2 (Sphere A)
__m/s2 (Sphere B)
(c) A long time after you cut the string, what is the speed of each sphere?
__m/s (Sphere A)
__m/s (Sphere B)

Homework Equations



V=U/q
V=-W/q
V=kq/r
U=kq/r^2
K=.5mv^2

The Attempt at a Solution



My teacher told me to use conservation of energy and momentum.

a) U=kq^2/r
U=((9*10^9)(4.50 µ)^2/1
U=.18225 Ji don't understand part B-C
 
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  • #2
For b), find the force acting on both particles and use Newton's First Law to find the accelerations.

For c), use conservation of momentum and energy. What is the potential energy when the particles are very far away? How are the velocities related? ehild
 

1. What is "electric potential"?

Electric potential is a measure of the amount of electrical potential energy that a charged particle possesses at a certain point in an electric field. It is often referred to as the potential difference between two points and is measured in volts (V).

2. How is electric potential calculated for tiny spheres?

The electric potential of a tiny sphere is calculated using the equation V = kQ/r, where V is the electric potential, k is the Coulomb's constant, Q is the charge of the sphere, and r is the distance between the sphere and the point where the potential is being measured. This equation assumes a point charge for the sphere and is valid for spheres with a radius much smaller than the distance r.

3. What factors affect the electric potential of tiny spheres?

The electric potential of a tiny sphere is affected by its charge, the distance between the sphere and the point where the potential is being measured, and the medium in which the sphere is located. The electric potential will increase as the charge of the sphere increases and decrease as the distance or the permittivity of the medium increases.

4. How does the electric potential of tiny spheres relate to the electric field?

The electric potential of tiny spheres is closely related to the electric field. The electric field is the force per unit charge experienced by a charged particle in an electric field, while the electric potential is the potential energy per unit charge. The electric field can be calculated from the electric potential using the equation E = -∇V, where ∇ is the gradient operator.

5. Can the electric potential of tiny spheres be negative?

Yes, the electric potential of tiny spheres can be negative. In fact, the electric potential of a negatively charged sphere will be negative, while the electric potential of a positively charged sphere will be positive. This is because the electric potential is a measure of potential energy and can be positive or negative depending on the direction of the electric field and the charge of the sphere.

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