A half circle arc with its center at the origin has a linear charge density of λ = 12 nC/m along the arc. The radius of the arc
is R = 3 cm. (a) What are is the electric field (magnitude and direction) at the origin? (b) What is the electric potential, V , at the origin?
1 answer:
Answer:
Explanation:
Given that,
Charge density is λ = 12 nC/m
And radius 3cm
r=0.03m.
The charge density of a along a circular arc is given as
λ= Q/πr
Then, Q=πrλ
Q=π×0.03×12×10^-9
Q=1.131×10^-9 C
Q=1.131 nC
Then, electric field along x axis is symmetrical and if cancels out
Now, Ey is in the negative direction
Electric field is given as,
Ey=-2kQ/πr²
K is constant =9×10^9Nm²/C²
Ey=-2×9×10^9×1.131×10^-9/(π ×0.03²)
Ey=7200 N/C.
The direction is negative direction of y axis, check attachment for diagram.
b. Electric potential at the origin is given as
V=Ed
d=r=0.03
V=7200×0.03
V=216V
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Answer:
- a) See explanation below
- b) At X.
Explanation:
Please, see the picture attached with the image of the plastic bottle for this question.
<u>(a) Explain why the water could not flow out of the bottle.</u>
What makes the water flow out of the botlle is the force of gravity, whic attracts the water towards the Earth.
When Johnson made a small hole at the bottom of the plastic bottle containing water, the air outside the bottle, which surrounds it and exerts a pressure all over the outer walls of the bottle, exerted a force against the small area of water "over" the hole that is in contact with the air.
Thus, this force of the air pushing upward through the wall opposed the force of gravity pulling downward making the net force zero and the water cannot fall.
<u>(b) To make the water flow out more easily, his teacher suggested making another hole. At which position - X, Y or Z, should he make the 2nd hole in order for the water to flow out the fastest?</u>
You must open the hole at a place where there is not water but air, such that the outer air can enter in the bottle.
That will make that the pressure in the space over the water inside the bottle be equal to the pressure outside.
The pressure of the air above the water will push it downward. Now, the force from the pressure of air inside the water, which is downward, opposes the upward force from the pressure of air around the first hole, and the net force will be downward, making the water flow out more easily.
Thus, the position where he should make the second hole in order for the water to flow fastest is at X.
