Given are the 3 charges: q1 = +10 µC, q2 = +20 µC, q3 = - 30 µC. All 3 are located at x = -1.0 m, at the origin.and at at x = +2.0 m, respectively. Find the Net Force on q2.

Question

Given are the 3 charges: q1 = +10 µC, q2 = +20 µC, q3 = - 30 µC. All 3 are located at x = -1.0 m, at the origin.and at at x = +2.0 m, respectively. Find the Net Force on q2.A. 3.15 N to the positive x- direction

B. 2.50 N to the negative x- direction

C. 3.3 N to the negative x-direction

D. 5.60 N to the positive x- direction

Referring to the problem above, Calculate the magnitude of the net electric field at(+1.0 m, 0) due to the 3 given charges.A. 189, 562 N/C

B. 386, 438 N/C

C. 675,500 N/C

D. 472,500 N/C

Answer 1

In order to find the net force on q2, we need coulomb's law, F=k|qA||qB|/r^2, where qA and qB the two charges repelling or attracting, and r is the distance from qA to qB.

Coulombs law can only be used to compute the force between two, and only two charges. The force on q2 is therefore a result of the force from q1 and q3 individually.

Since charge q1 ia positive and q2 is also positive they will repel, putting a positive (rightward pointing) force on q2 due to q1 of magnitude F_21= kq1q2/(1)^2 = (9*10^9)*(10*10^-6)*(20*10^-6)/(1^2)=1.8 N right

Since q3 is negative q2 and q3 will attract, putting a positive (right facing) force on q2 of magnitude F_23 = kq2q3/(2^2) = (9*10^9)*(30*10^-6)*(20*10^-6)/(2^2) = 1.35 N right

So the net force on q2 is +1.35+1.8=3.15 N to the right.

The electric field is calculated in a similar manner, E=k|qA|/r^2 where qA is the charge producing the E field and r is the distance from qA to the point in where we want to know the electric field. Positive electric fields lines radiate outward, while negative electric field lines go inward. At 1m, E1 , E2 and E3 will all point to the right.

So Enet = E1+E2+E3 = kq1/2^2 + kq2/1^2 +kq3/1^2 = (9*10^9)(10^-6)(10/4 + 20 + 30) = 472500 N/C

Note that all charges are in absolute values, as it is easiest to determine direction and fix the sign for each term.