A group of science and engineering students embarks on a quest to make an electrostatic projectile launcher. For their first trial, a horizontal, frictionless surface is positioned next to the 12-cm-diameter sphere of a Van de Graaff generator, and a small, 5.0 g plastic cube is placed on the surface with its center 2.0 cm from the edge of the sphere. The cube is given a positive charge, and then the Van de Graaff generator is turned on, charging the sphere to a potential of 200,000 V in a negligible amount of time. How much charge does the plastic cube need to achieve a final speed of a mere 3.0 m/s? Does this seem like a practical projectile launcher?
The required Charge is 150 nC
As per the law of energy conversations, within a closed system energy remains same. Energy cannot be destroyed or created it only transform from one form to another.
The expression in this electric potential is;
Here in in equation K is column's constant and q is the charge where r denote as distance.
Sphere potential is 200,000 V
d =12 cm, hence r= 6 cm
and k= 9 x 109 Nm2/C2
As per the given Condition distance is;
d=2 cm+ 6cm =8 cm
hence the potential difference is;
Substituting all the given data along with the distance of condition;
As law of energy conversations;
kinetic energy is equal to potential energy
As per given condition m= 5g; v= 3 m/s
Hence the required charge can be considered as 150 nC
In proton-beam therapy, a high-energy beam of protons is fired at a tumor. As the protons stop in the tumor, their kinetic energy breaks apart the tumor’s DNA, thus killing the tumor cells. For one patient, it is desired to deposit of proton energy in the tumor. To create the proton beam, protons are accelerated from rest through a potential difference. What is the total charge of the protons that must be fired at the tumor?
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