Three charges are placed as shown. The value of q1 is 2.2 C and the value of q3

Question

Three charges are placed as shown. The value of q1 is 2.2 C and the value of q3 is -4.0 C. The net force on q3 is in the negative x-direction.

Part A) Determine the charge on q2.

The sum of the vertical components of the two electric forces on q3 must be 0.

so far I have found the following information I know for sure to be correct:

Angle between q1q2 and q1q3: 36.92°

Angle between q2q1 and q2q3: 47.67°

Magnitude of force between q1 and q3: 42.83 N

however I have been unable to finish the problem and find the answer

so far I have tried the following values which have been incorrect

1.800 uC

-1.456 uC

-1.802*10-6 C

-1.802 uC

1.802 uC

1.802*10-6 uC

-1.29*10^-27 uC

2.654*10^-12 uC

1.802*10^-12 uC

Part B) Determine the magnitude of the net force on q3

The sum of the vertical components of the two electric forces on q3 must be 0.

Explanation / Answer

theta 1 : angle of q1 in the triangle

from the cosine formula cos (theta 1) = (5.8^2 + 4.3^2 - 3.5^2) / (2*5.8*4.3) = 0.8

theta 1 = 36.92 degree

similerly theta 2 : angle of q2 in the triangle = cos^(-1)[( 5.8^2 + 3.5^2 - 4.3^2) / (2*3.5*5.8)] = 47.56 degree

A)

F13 = force due to q1 on q3 is directed towords q1 and = {kq1q3 / (4.3)^2} ( - cos36.92 i - sin 36.92 j)

F13 = {(9*10^9 * 2.2 * 4 * 10^(-12)) / (4.3*10^(-2))^2 } ( - cos36.92 i - sin 36.92 j)

= (- 3.42 i - 2.57 j) * 10 N

F23 = directed towords q3 so that vertical component has to cancelled with F13 j component

q2 has the same sign as q3 ( - )

F23 j + F13 j = 0

F23 j = 2.57 *10 = [kq2q3 / (3.5*10^(-2))^2] sin(47.56)

q2 = - 2.57*10 * 3.5^(2)*10^(-4) / (9*10^9 * 4 * 10^(-6) * sin47.56)

= - 1.18 * 10^(-6) C

B)

F23 i = - [ kq2q3 / ((3.5*10^(-2))^2) ] cos47.56 i

= - (9*10^9 * 1.18 * 4 * 10^(-12) * cos47.56) / (3.5^2*10^(-4)) i

= - 2.34 * 10 N i

so net forse in x direction is

F13 i + F23 i = (- 3.42 - 2.34 ) * 10 = - 5.76 * 10 N i

so magnitude of the force is 57.6 N

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.