A point charge q1 = 4.0 ?C is at the origin and a point charge q2 = 6.0 ?C is on

Question

A point charge q1 = 4.0 ?C is at the origin and a point charge q2 = 6.0 ?C is on the x axis at x = 3.0 m. (a) Find the electric force on charge q2. (b) Find the electric force on q1. (c) How would your answers for Parts (a) and (b) differ if q2 were -6.0 ?C?

I am looking for a more detailed answer to the the last part. The vector is on dimensional or essential has just a radius of 3. With this information, how come we are not using Coulombs Law with the absolute value of (q1 x q2) to find the F12 and F21 for -6.0 ?C?

When would we use the k*abs value(q1q2)*r/ (mag r)^3 vs. the kq1q2(directional vector with ai,bj,ck)/(mag dir veector)^3

Explanation / Answer

E_ = q/(4p e0 r^2) e_r where 1/(4p e0) = 8.9874*10^9 N m^2 / C^2, E_ is the E-field vector, and e_r is the unit vector in the r direction (from the charge q to the point where the field is observed). Since e_r = r_ / r = (x/r, y/r), the x-component of E is E_x = q x/(4p e0 r^3) For the given points, r_ = (4.00, -3.00) m r = 5.00 m x = 4.00 m and E_x = (8.987*10^9 N m^2 / C^2) (-4.00 nC) 4/5^3 = -143.8/125 N/C = -1.150 N/C 2.) Charges of opposite sign, on opposite sides of the given point, will contribute field strengths in the same direction at that point. Both will lie in the -x direction. q1 = -3.0nC q2 = 11.0nC r1 = r2 = 4.00m E_x = (q1/r1^2 - q2/r2^2)/(4p e0) = (8.9874*10^9 N m^2 / C^2) (-14.0nC)/(16.00m^2) = magnitude of 7.86 N/C in the -x direction 3.) Somewhere on the y-axis is such a point. Since both charges are negative, they both "pull" the field toward themselves. We must find out where those pulls are equal. q1 = -6.5µC; y1 = 6.0m q2 = -8.5µC; y2 = -4.0m At y, the magnitude of the field, which we want to be 0, is 0 = E = E_y = (q1/r1^2 - q2/r2^2)/(4p e0) 0 = q1/(y - y1)^2 - q2/(y - y2)^2 Note that (y - y1) < 0 and (y - y2) > 0, so when taking the square root to solve this, we must go: (y1 - y)/(y - y2) = v(q1/q2) = v(13/17) = 0.8744746 = a y = (y1 + a y2)/(1 + a) = 1.335 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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