A bug crawls 3.0 mm east, 4.0mm north, and then 5.0 mm at 45 north of east. Draw a diagram showing its displacements and determi
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Answer:
The total electric potential at mid way due to 'q' is
The net Electric field at midway due to 'q' is 0.
Solution:
According to the question, the separation between two parallel plates, plate A and plate B (say) = d
The electric potential at a distance d due to 'Q' is:
Now, for the Electric potential for the two plates A and B at midway between the plates due to 'q':
For plate A,
Similar is the case with plate B:
Since the electric potential is a scalar quantity, the net or total potential is given as the sum of the potential for the two plates:
Now,
The Electric field due to charge Q at a distance is given by:
Now, if the charge q is mid way between the field, then distance is .
Electric Field at plate A, at midway due to charge q:
Similarly, for plate B:
Both the fields for plate A and B are due to charge 'q' and as such will be equal in magnitude with direction of fields opposite to each other and hence cancels out making net Electric field zero.
Answer: 313920
Explanation:First, we’re going to assume that the top of the circular plate surface is 2 meters under the water. Next, we will set up the axis system so that the origin of the axis system is at the center of the plate.
Finally, we will again split up the plate into n horizontal strips each of width Δy and we’ll choose a point y∗ from each strip. Attached to this is a sketch of the set up.
The water’s surface is shown at the top of the sketch. Below the water’s surface is the circular plate and a standard xy-axis system is superimposed on the circle with the center of the circle at the origin of the axis system. It is shown that the distance from the water’s surface and the top of the plate is 6 meters and the distance from the water’s surface to the x-axis (and hence the center of the plate) is 8 meters.
The depth below the water surface of each strip is,
di = 8 − yi
and that in turn gives us the pressure on the strip,
Pi =ρgdi = 9810 (8−yi)
The area of each strip is,
Ai = 2√4− (yi) 2Δy
The hydrostatic force on each strip is,
Fi = Pi Ai=9810 (8−yi) (2) √4−(yi)² Δy
The total force on the plate is found on the attached image.
