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Chrome File Edit View History Bookmarks People Window Help 81% D Tue 1:10 AM Mastering Physics: HW 1 Secure https Sessio mastering physi cs.com/ next&assignment; ProblemID 77464110 Physics 2200 New Problem 21.62 Resources previous l 10 of 12 l next MasteringPh Problem 21.62 Part A My Courses Two identical spheres with mass m are hung from silk Suppose that the angle is small, and find the equilibrium separation d between the spheres (Hint: lf is small, then threads of length L, as shown in the figure (Figure 1) Course Home Each sphere has the same charge, so g -g2 The Express your answer in terms of the variables g, L, m and appropriate constants. radius of each sphere is very smallcompared to the Syllabus distance between the spheres, so they may be treated as point charges. Assignments Course Tools igure eText Submit My Answers Give U Student Solut incorrect; Try Again; 5 attempts remaining Manual Study Area Continue User Settings mass m mass m charge q charge q2 Learn more about assinnment sonres

Explanation / Answer

As both the spheres are in Equilibrium, the Net force acting on each sphere is 0.

Tension, T , Electrostatic Force, Fe and Gravitational force Fg are acting on each sphere.

Fe & Fg must balance the Tension, T for Equilibrium.

Tension acts along the line of the string.

Hence, the Resultant of Fe and Fg must act along the same line for Equilibrium.

Hence, tan = Fe/Fg

Fe = (K* q1*q2)/ d2 , where

K = (1/4 ),

q1=q2=q

d= Distance between 2 spheres

Now, Fg= mg

Also, in a single Triangle,

tan = sin = Half the distnace btwn 2 spheres/ L

-> sin = d/2L

-> Fe/Fg= d/2L

-> Kq2/( d2 )*(mg) = d/2L

-> d3 = 2LKq2/ mg =( q2L/ 2 mg)

-> d = ( q2L/ 2 mg) is the required distance for Equilibrium.

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