# Problem: A 2.5 mm -diameter sphere is charged to -4.6 nC. An electron fired directly at the sphere from far away comes to within 0.35 mm of the surface of the target before being reflected.A. What was the electron's initial speed?B. At what distance from the surface of the sphere is the electron's speed half of its initial value?C. What is the acceleration of the electron at its turning point?

###### FREE Expert Solution

Law of conservation of energy:

$\overline{){{\mathbf{K}}}_{{\mathbf{i}}}{\mathbf{+}}{{\mathbf{U}}}_{{\mathbf{i}}}{\mathbf{+}}{{\mathbf{W}}}_{{\mathbf{nc}}}{\mathbf{=}}{{\mathbf{K}}}_{{\mathbf{f}}}{\mathbf{+}}{{\mathbf{U}}}_{{\mathbf{f}}}}$, where Wnc is the work done by non-conservative forces such as gravity.

Electrostatic potential energy:

$\overline{){\mathbf{U}}{\mathbf{=}}\frac{\mathbf{k}{\mathbf{q}}_{\mathbf{1}}{\mathbf{q}}_{\mathbf{2}}}{\mathbf{r}}}$

Kinetic energy:

$\overline{){\mathbf{K}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{{\mathbf{mv}}}^{{\mathbf{2}}}}$

Newton's second law:

$\overline{){\mathbf{\Sigma }}{\mathbf{F}}{\mathbf{=}}{\mathbf{m}}{\mathbf{a}}}$

Coulomb's law:

$\overline{){\mathbf{F}}{\mathbf{=}}\frac{\mathbf{k}{\mathbf{q}}_{\mathbf{1}}{\mathbf{q}}_{\mathbf{2}}}{{\mathbf{r}}^{\mathbf{2}}}}$

81% (316 ratings) ###### Problem Details

A 2.5 mm -diameter sphere is charged to -4.6 nC. An electron fired directly at the sphere from far away comes to within 0.35 mm of the surface of the target before being reflected.

A. What was the electron's initial speed?

B. At what distance from the surface of the sphere is the electron's speed half of its initial value?

C. What is the acceleration of the electron at its turning point?