Problem 16.16 11 of 11> tants Part A A large electroscope is made with \"leaves\

Question

Problem 16.16 11 of 11> tants Part A A large electroscope is made with "leaves" that are 78-cm-long wires with tiny 23 g spheres at the ends When charged, nearly all the charge resides on the spheres If the wires each make a 26 angle with the vertical (Figure 1), what total chargeQ must have been applied to the electroscope? Ignore the mass of the wires Express your answer to two significant figures and include the appropriate units Figure 6°126 78 cm 78 cm Q 0.050 Submit Previous Answers Request Answer Incorrect, Try Again: 3 attempts remaining

Explanation / Answer

Here from the given diagram the tension is resolved into two components

Tsintheta =k(q/2)2/l2-------------(1)

and Tcostheta =mg---------------(2)

Now from the above two equations we get

tantheta =k(q/2)2/mgl2===> q2 =Tantheta4mgl2/k

Then the total charge is given by q =Sqrt[4mgl2*tantheta/k]

=Sqrt[Tan(26)*4*23*10-3*9.8*(78*10-2)2/9*109]

=545.219*10-8C

=5.452*10-6C

=5.452uC

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