Answer to Question #285081 in Electricity and Magnetism for Dddddd

Question #285081

shows an arrangement of four charged particles, with angle θ = 30.0° and 

distance d = 2.00 cm. Particle 2 has charge q2 = +8.00 × 10-19 C; particles 3 and 4 have charges q3

= q4 = -1.60 × 10-19 C. (a) What is distance D between the origin and particle 2 if the net 

electrostatic force on particle 1 due to the other particles is zero? (b) If particles 3 and 4 were 

moved closer to the x axis but maintained their symmetry about that axis, would the required 

value of D be greater than, less than, or the same as in part (a)?


1
Expert's answer
2022-01-06T10:47:52-0500

d=2.00cm

"\\theta=30\u00b0\\\\q_2=8\\times 10^{-19}c\\\\q_3=q_4=-1.6\\times 10^{-19}c"


"r=\\frac{2d}{\\sqrt{3}}"

Net force on q1 due to to the to charge q3 q4 on the y-axis has magnitude of force

"F=2\\frac{q_1q_3}{4\\pi \\epsilon_0 r^2}cos30\u00b0"

"q_2=8.00\\times10^{-19}c=5.00|q_3|" then net force will be zero

"\\frac{3\\sqrt {3}q_1q_3}{16\\pi\\epsilon_0 d^2}=\\frac{q_1q_2}{4\\pi \\epsilon(D+d)^2}"

"D=d(2\\sqrt{\\frac{ 5}{3\\sqrt{3}}}-1)"

"D=0.9245d"

d=2.00cm

"D=1.8490cm"

(B) If particles 3 and 4 were


moved closer to the x axis but maintained their symmetry about that axis, would the required


value of D be greater than

"\\theta" Varying then D increase

We can say D will be greater then part (a)

"D>1.8490cm"


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