Question

Four Charges Part A Four charges Aq,Bq,Cq, and Dq (q 2.00 x 107c) sit in a plane at the corners of a square whose sides have length d 23.0 cm, as shown in the diagram below. A charge, Eq, is placed at the origin at the center of the square. Aq Bq Eq Dg Cq oquaro of side longth,d DATA: A = 4, B = 8, C = 5, D = 2, E = 4. Consider the charge at the center of the square, what is the net force, in the x-direction, on this charge? palt Submit Answer Incorrect. Tries 1/6 Previous Tries Part B What is the net force, in the y-direction, on the center charge? 5.77+1012N Submit Answer Incorrect. Tries 2/6 Previous Tries Part C Consider the situation where A B-C-D-1,E--1. For each of the following statements determine whether it is true or false. The sum of the forces on the center charge in the x-direction equals zero. The sum of the forces on the center charge in the y-direction equals zero. If one were to double the magnitude of the upper-right-hand positive charge, the negative charge would not be in equilibrium. The equilibrium point at the center is a stable equilibrium for the motion of the negative charge in the plane of the square. B If one were to triple the magnitude of the negative charge, the negative charge would be in equilibrium. The equilibrium point at the center is a stable equilibrium for the motion of the negative charge in the line from the center charge and perpendicular to the plane of the square Submit Answer Tries o/6

answers are not -4.98*10^12 N for part A

or -5.77 *10^12 N for part B

Answer 1

Part A :

According to the question,

Charge at A = 4q

Charge at B = 8q

Charge at C = 5q

Charge at D = 2q

Charge at E = 4q

Where, q = 2.00 x 10^-7 C

Given, AB =BC =CD =DA = 23 cm (sides of square)

And AE = BE =CE = DE = r (say)

We can calculate the value of r as

so,  

Now, we can calculate the force on the charge E due to each and every charge at the corners of square :

Force on E due to the charge at A is

   towards the point (or corner) C

Force on E due to the charge at B is

   towards the point D

Force on E due to the charge at C is

   towards the point A

Force on E due to the charge at D is

towards the point B

Here all forces are in Newton .

Here, we can see that the forces F_AEand F_CE are on the same line. So, we can calculate the net magnitude of force on charge at E due to these two forces as

   towards the point A.

And, Similarly due to the forces F_BE and F_DE as

towards the point D.

Here,

     

So,

So, the new diagram will look like

From this diagram, we can write

and

So, the net force F_net on the charge at E due to all other charges can be given as

(symbols without arrow are showing magnitude of the vectors)

  

Putting the value of kq² / r² , we get

So, the net force in x - direction is -0.269 N on the given charge (at E) .

Part B :

Net force in y direction on the charge at E is -0.192 N .

Part C :

If A = B = C = D = 1 and E = -1

Then net force will cancel out each other. i.e.

So, F_x = F_y = 0

And all the statements are true except the fourth one. i.e. the equilibrium point at center is not a stable equilibrium for the motion of the negative charge in the plane of the square.

For any doubt please comment.