i Four point charges are located at the corners of a square

i. Four point charges are located at the corners of a square with length a 20m as shown in the figure. If B 4q. C 6q and q 2 nc find the magnitude of the net electric field at the center of the square. a) 6.4x103 N/C b) 0 c) 1.1x104 NIC d) 4.5x105 NC. 2.A parallel-plate capacitor with an area o.s m2 and plate separation of 6 mm is connected to a 12 v battery. How much charge is stored on the plates? d) 890 nC c)0.89 nC b) 89 nC a) 8.9 nC 3. Replacing a wire resistor with another of the same material and length but with three times the diameter will have the effect of changing the resistance by what factor? d)9 c) 3 b) 119 a) 1/3

Solution

1)

Electric fields due to both the charges denoted as B cancel each other out at the center.

Now due to other two charges,

Enet = k*(6q - q)/(a/sqrt(2))^2

= 9*10^9*(5*2*10^-9)/(0.02^2/2)

= 4.5*10^5 N/C

2)

C = epsilon*A/d

= 8.854*10^-12*0.5/0.006

= 7.38*10^-10

So, charge, Q = C*V

= 7.38*10^-10*12

= 8.86*10^-9 C

= 8.9 nC

3)

Resistance is given by:

R = rho*L/A

As the diameter is tripled, area(A) is 3^2 = 9 times

So, R is 1/9 times <--- answer