Three point charges are fixed to the corners of a square, one to a corner, in such a way that the net electric field at the empty corner is zero. Do these charges all have (a) the same sign and (b) the same magnitude (but, possibly, different signs)? Which of the following are true?
1. Since the field at the empty corner due to the charge placed at the diagonally opposite corner will have equal x and y components, the charges placed at the other two corners must have the same magnitude.
2. It is certainly possible for all three occupied corners of the square to have charges with the same magnitude and still produce a zero electric field at the un-occupied corner of the square.
3. It is impossible to have any arrangement of charges, with any combination of sign and magnitude, at 3 of the 4 corners of a square such that the electric field at the un-occupied corner iszero.
4. The charge placed at the diagonally opposite corner to the empty corner must have a charge opposite in sign to the identical charges placed at the other occupied corners; and have a charge whose magnitude is larger than that of the other two charges.
5. The charges placed at the two corners along the edge of the square away from the empty must have the same sign. In that way the net field at the empty cornerdue to the two charges alone will lie along the diagonal of the square.
6. It is certainly possible for all three charges at the occupied corners of the square to have the same sign and still produce zero field at the un-occupied corner of the square.

1.- No

2.-No

3.-No

The arrangement below make it possible

4.-Yes

As describe in step by step explanation

5.-They need to have the same sign, because this is the only way you can compensate with other opposite charge

6.-No

Explanation:

We have to reasoning this way. Let say the empty corner is at the upper right of the square. if we call F1 and F2 forces acting in this point, due to charges of the left and down corners of the square respectivly. F1 will have direction of x axis and F2 will have direction of y axis. Now in order to cancel these two forces, we need:

1.-Charges in left  and down coners, must be of the same sign and magnitude

2.-the charge in diagonal opposite corner have to be of opposite sign and bigger charge than the two previous charges.

How big it need to be ??

E₁  = Ex  =  K*q₁/d²      E₂  =  Ey  = K*q₂/d²   (1)       q₁  =  q₂  =  q

distance between empty corner and its opposite corner is:

L = √ d² + d²   ⇒ L  = √2 * d

cos 45⁸ = sin 45⁸ = √2/2

E₃  ( field due to charge in opposite corner) is:

E₃ =K* q/ 2 * d²  

And  E₃ₓ  =  E₃y  =  cos 45⁸* E₃

E₃ₓ  = [ K*q/2 *d² ]* √2/2

E₃ₓ  =  K*q *√2/4*d²

Now if we compare   E₃ₓ   with   Ex  =  K*q₁/d²    equation (1)

q*√2/4  = q₁

then

q = 4*q₁/√2

carbon is found in all living things. carbon atoms move constantly through

living organisms, the oceans, the atmosphere, and the earth’s crust in what is

known as the carbon cycle. the directions taken by carbon atoms through this

cycle are very complicated and can take millions of years to make a full circle.

all animals, from humans to the dinosaurs are part of the carbon cycle. when

animals eat food, they get carbon in the form of carbohydrates and proteins.

in animals, oxygen combines with food in the cells to produce energy for daily

activity and then gives off carbon. the carbon combines with oxygen to form

carbon dioxide (co2) and is released back into the atmosphere as a waste

product when animals breathe and exhale.

from 145-65 million years ago, earth was much

hotter than today and covered with dense,

tropical swamp forests. the trees and other

plants were immense and

provided an endless supply of

food for the giant animals that

roamed the land. somewhere in

the air above one of these

forests, a lone carbon atom has joined

up with two oxygen atoms to form a molecule of co2.

the co2 molecule was sucked into the tiny holes (stomata) on the leaf of a

fern plant and joined with sunlight, chlorophyll and water to make food and

energy in the plant’s cells through photosynthesis. the oxygen (o2) from the

co2 molecule was sent back into the atmosphere; the carbon atom (c) was

detached and used to make a molecule of sugar.

if that carbon atom had been eaten instead, a totally

different situation would have developed. let’s say

that a giant plant-eating dinosaur (herbivore) ate the

fern for breakfast, and swallowed the carbon in the

fern in the form of carbohydrates and proteins. in

the process of respiration, oxygen combined with

the carbohydrates and proteins in the dinosaur’s cells

to provide energy for its daily activity.  

two charges are fixed in place on the x-axis as shown. the charge at x = 0 is negative and has magnitude q = 2 μcoulombs (1 μcoulomb = 10-6 coulombs). the charge at x = d, (d = +12 cm), is positive and has magnitude q = 4 μcoulombs. find a point x = xo along the x-axis at which the electric field is zero.