Two spheres, one with charge Q-1 = -3 Times 10^-8 C and the other with charge Q_

Question

Two spheres, one with charge Q-1 = -3 Times 10^-8 C and the other with charge Q_2 = 5 Times 10^-8 C, are located 3m apart, as shown in the figure below. Point A is 1m from Q_1 and 2m from Q_2, and point B is 4m from Q_1 and 5m from Q_2. The angle Q_1-B-Q_2 is a right angle, and the angle Q_1-Q_2-B is 36.9 degree What is the electric field at point A. and what is the electric field at point B? (Give your answers as either magnitudes and directions or in terms of x and y components.) What is the potential difference between points A and B?

Explanation / Answer

q1 = - 3 * 10^-8 C
q2 = 5 * 10^-8 C

(a)
Electric Field at point A,
Ea = - k*q1/r1^2 i^ - k*q2/r2^2
Ea = - (8.9*10^9*3 * 10^-8)/1 i^ -  (8.9*10^9*5 * 10^-8)/2^2 i^
Ea = - 378.25 i^ N/C

Electric Field at point B,
Eb =  k*q1/r1^2 j^ -  k*q2/r2^2 * cos(36.9) j^ -  k*q2/r2^2 * sin(36.9) i^
Eb = (8.9*10^9*3 * 10^-8)/4^2 j^ - (8.9*10^9*5 * 10^-8)/5^2 * cos(36.9) j^ - (8.9*10^9*5 * 10^-8)/5^2 * sin(36.9) i^
Eb = 10.69 i^ - 2.45 j^ N/C

(b)
Potential At Point A,
Va = k*q1/r1 + k*q2/r2
Va = - (8.9*10^9*3 * 10^-8)/1 + (8.9*10^9*5 * 10^-8)/2
Va = -44.5 V

Potential At Point B,
Vb = k*q1/r1 + k*q2/r2
Vb = - (8.9*10^9*3 * 10^-8)/4 + (8.9*10^9*5 * 10^-8)/5
Vb = 22.25 V

Vb - Va = 22.25 + 44.5
Vb - Va = 66.75 V

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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