The figure below shows a plastic ring of radius R 46.0 cm. Two smal charged bead

Question

The figure below shows a plastic ring of radius R 46.0 cm. Two smal charged beads are on the ring: Bead 1 of charge +2.00 Cis ed pace at the eft. side: bead of charge +5.90 uC can be moved along the ring. The two beads produce a net electric field of magnitude E at the center of the ring. At what positive and negative values of angle should bead 2 be positioned such that E = 2.00 x 105 N/C? (Measure the angle from the positive x axis taking counterclockwise to be positive.) positive angle negative angle counterclockwise from the +x-axis counterclockwise from the +x-axis Ring Bead 2 Bead 1

Explanation / Answer

By law of cosines,

E² = [k(q1)/R²]² + [k(q2)/R²]² - 2[k(q1)/R²][k(q2)/R²]cos

(2.00e5 N/C)² R^4 / k² = (q1)² + (q2)² - 2(q1)(q2)cos

(2.00e5 N/C)² (0.460 m)^4 / (9.00e9 N-m²/C²)² = (2.00e-6 C)² + (5.90e-6 C)² - 2(2.00e-6 C)(5.90e-6 C)cos

cos = 0.707589

= ±45°

Thus,

positive angle = 45° ccw from +x axis

Negative angle = 360 – 45 = 315°ccw from +x axis

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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