7. Two point charges are held at the comers of a rectangle as shown in the figur

Question

7. Two point charges are held at the comers of a rectangle as shown in the figure. The lengths of the sides of the rectangle are 5 em and 15 cm. Assume that the electric potential is defined to be zero at infinity. (The distance is in unit of cm.) (a) (10 pts.) Find the magnitude and direction (angle )of the force on the +2 uC charge. (HINT: In-Cass Exercise 1, Look at Class 3 Slide 11-18') +2.0 C (b) (10 pts ) What s the magnitude and direction (angle ) of the electric field at position A by two point charges? (HINT: In-Class Exercise 3. Look at 'Class 5 Slides 12-13') 2 +2.0 C

Explanation / Answer

a)
magnitude of force,

F = k*q1*q2/d^2

= 9*10^9*2*10^-6*5*10^-6/(0.05^2 + 0.15^2)

= 3.6 N

direction : theta = tan^-1(5/15)

= 18.4 degrees above -x axis

= 161.6 degrees from +x axis in counter clockwise direction .

b)

E1 = k*q1/r1^2

= 9*10^9*2*10^-6/0.05^2

= 7.20*10^6 N/c

E2 = k*q2/r2^2

= 9*10^9*5*10^-6/0.15^2

= 2.0*10^6 N/c

Enet = sqrt(E1^2 + E2^2)

= sqrt(7.2^2 +2^2)*10^6

= 7.47*10^6 N/c

direction : theta = tan^-1(E1/E2)

= tan^-1(7.2/2)

= 74.5 degrees above - xaxis

= 105.5 degrees with +x axis in counterclockwise direction

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