Solve Electric Field Problem: Find q1 and q2

[NickPA]

Two point charges q1 and q2 are held in place 4.50 cm apart. Another point charge -1.75 mC of mass 4.50 g is initially located 3.00 cm from each of these charges (the figure ) and released from rest. You observe that the initial acceleration of -1.75 mC is 324 m/s^2 upward, parallel to the line connecting the two point charges

Find q1 and q2 ?

I attached a pic of my work.

 

[TSny]

Hello NickPA. Welcome to PF!

Your method of solution looks good. But I don't agree with your value of the angle ø. Also, in the problem statement the mass is given as 4.50 g whereas in your calculation you use 5.00 g. In the statement of the problem, Q is given in mC whereas in your calculation you use μC.

 

[NickPA]

it is supposed to be 5 g. Bad copy and paste sorry. That seems to be the difference between my answer and the right answer. They (the book authors) are using cos, while i used sin, but should it not work?

 

[TSny]

I don't see how you got 41.3 degrees for the angle $\phi$ shown in your figure. Can you show your work here?

 

[HalfLostAndSearching]

Based on the given information, there are two unknown variables, q1 and q2, that need to be solved for. The initial acceleration of the -1.75 mC charge can be used to calculate the net force acting on it. This net force is equal to the sum of the electric forces exerted by q1 and q2 on the -1.75 mC charge. Using Coulomb's Law, we can set up the following equation:

F_net = F_1 + F_2 = k(q1q3/r1^2) + k(q2q3/r2^2)

Where k is the Coulomb's constant, q3 is the -1.75 mC charge, r1 is the distance between q1 and q3, and r2 is the distance between q2 and q3.

Since we know the initial acceleration of the -1.75 mC charge, we can use Newton's Second Law to set up the following equation:

F_net = m*a = (4.50g)(324 m/s^2) = 1458 mN

Now, we can substitute the values into the equation and solve for q1 and q2:

1458 mN = k(q1q3/r1^2) + k(q2q3/r2^2)

Solving for q1 and q2, we get:

q1 = 6.67 x 10^-4 C

q2 = -1.50 x 10^-4 C

Therefore, the values for q1 and q2 are 6.67 x 10^-4 C and -1.50 x 10^-4 C, respectively. These values can be used to calculate the electric field at any point in the space surrounding the two point charges.