In: Physics
A particle is uncharged and is thrown vertically upward from
ground level with a speed of 23.1 m/s. As a result, it attains a
maximum height h. The particle is then given a positive
charge +q and reaches the same maximum height h
when thrown vertically upward with a speed of 27.3 m/s. The
electric potential at the height h exceeds the electric
potential at ground level. Finally, the particle is given a
negative charge −q. Ignoring air resistance, determine the
speed with which the negatively charged particle must be thrown
vertically upward, so that it attains exactly the maximum height
h. In all three situations, be sure to include the effect
of gravity.
m/s
Two point charges, +3.06 µC and -6.20 µC, are separated by 1.10
m. What is the electric potential midway between them?
V
PROBLEM 1:
Let us assume at the ground level the potential energy due to gravitation and the electric potential are zero.
Now, the total energy of the uncharged particle at the ground level is
And the energy of the uncharged particle at the maximum height h is (the kinetic energy at this point becomes zero)
The conservation of energy gives us
So the maximum height is 27.225 m.
Now, when the particle is charged
The energy of the positively charged particle at the ground level is
And the energy of the positively charged particle at height h is
Putting the value of h
Conservation of energy gives us
So, the potential at height is 105.84m/q.
Now,
The energy of the negatively charged particle at the ground level is
And the energy of the negatively charged particle at the height h is
Putting the values of h and V in the above equation
The conservation of energy gives us
So, the initial velocity of the negatively charged particle must be 17.94 m/s to reach the same height of h.
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PROBLEM 2:
The electric potential midway is
So, the potential is -51381.8 V.