Shows an arrangement of four point charges at the comers of a square of side a a

Question

Shows an arrangement of four point charges at the comers of a square of side a as shown The charges are given as q, 2q, 3q and 4q, where q = 4.0 times 10^6 C and a = 10 cm Calculate the magnitude of the force exerted by 2q on 4q Calculate the magnitude of the electric field due to 3q at the center Calculate total electric potential at the center of the square Calculate electric potential energy of the system of charges Fig-2 shows two plates separated by a distance of 2.00 mm and at potentials: V_1 = -70.0 V and 50.0 V as indicated. A proton moves from plate-1 to plate-2 with initial speed of 90.0 km/s

Explanation / Answer

1) Force between 2q and 4q,

F = k*2*q*4*q/(2*a^2)

= 4*k*q^2/a^2

= 4*9*10^9*(4*10^-6)^2/0.01^2

= 5760 N

2) E = k*3*q/(a^2/2)

= 6*k*q/a^2

= 6*9*10^9*4*10^-6/0.01^2

= 2.16*10^9 N/c

3) distance from each corner to center, r = sqrt(2)*a/2

= sqrt(2)*0.01/2

= 0.00707 m

Vnet = k*q/r + k*2*q/r + k*3*q/r + k*4*q/r

= 10*k*q/r

= 10*9*10^9*4*10^-6/0.00707

= 5.09*10^7 volts

4) U = 2*k*q^2/a + 3*k*q^2/sqrt(2)*a + 4*k*q^2/a + 6*k*q^2/a + 8*k*q^2/(sqrt(2)*a) + 12*k*q^2/a

= (k*q^2/a)*(1 + 3/sqrt(2) + 4 + 6 + 8/sqrt(2) + 12 )

= (9*10^9*(4*10^-6)^2/0.01)*(1 + 3/sqrt(2) + 4 + 6 + 8/sqrt(2) + 12 )

= 443 J

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