Please answer all the questions with brief explanations. Thank you. The four cas

Question

Please answer all the questions with brief explanations. Thank you.

The four cases below all show a ball with a charge of -3q at the top right corner of a square. Then there is either one, two, or three additional charged balls, each ball located at a different corner of the square -24 tg tq (a) Rank the cases based on the magnitude of the net electric field at the center of the square, from largest to smallest. (Use only >orsymbols. Do not include any parentheses around the letters or symbols.) For the rest of the problem, use q = 2.70 × 10-6 C, and L = 30.0 cm, as well as k = 8.99 x 109 N m2/C2. (b) In Case C, calculate the magnitude of the net electric field at the center of the square. 540072.09X N/C (c) In Case A, calculate the magnitude of the net electric field at the bottom left corner of the square. 540074.59 N/C

Explanation / Answer

a)

net electric field will be highest in the case A as the two forces are perpendicular to each other

then case C will come as electric field due to -3Q will appear at the center of the square

B and D will have same electric field

So, the ranking is as follows :

A > C > (B = D)

b)

Enet = k*(3q)/(L^2/2)

= 9*10^9*(3*2.7*10^-6)/(0.3^2/2)

= 1.62*10^6 N/C

c)

E1 = k*q/L^2

= 9*10^9*(2.7*10^-6)/0.3^2

= 2.7*10^5 N/C

E2 = k*(3q)/(2*L^2)

= 9*10^9*(3*2.7*10^-6)/(2*0.3^2)

= 4.05*10^5 N/C

So, Enet,x = 4.05*10^5*cos(45 deg)

= 2.86*10^5 N/C

So, Enet,y = 4.05*10^5*sin(45 deg) - 1.62*10^6

= 1.33*10^6 N/C

So, Enet = sqrt(1.33^2 + 0.286^2)

= 1.36*10^6 N/C <--------- answer

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