The figure below shows a plastic ring of radius R = 49.0 cm. Two small charged b

Question

The figure below shows a plastic ring of radius R = 49.0 cm. Two small charged beads are on the ring: Bead 1 of charge +2.00 C is fixed in place at the left side; bead 2 of charge +5.50 C 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 = 2.00 105 N/C? (Measure the angle from the positive x axis taking counterclockwise to be positive.)

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 (0.490 m)^4 / (9.00e9 N-m²/C²)² = (2.00e-6 C)² + (5.50e-6 C)² - 2(2.00e-6 C)(5.50e-6 C)cos

cos = 0.99
= ±25.8°

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