A small sphere with mass 2.20 g hangs by a thread between two large parallel ver

Question

A small sphere with mass 2.20 g hangs by a thread between two large parallel vertical plates 5.00 cm apart (Figure 1) . The plates are insulating and have uniform surface charge densities + and . The charge on the sphere is q = 7.70×106 C . Part A What potential difference between the plates will cause the thread to assume an angle of 30.0 with the vertical? The vertical deflecting plates of a typical classroom oscilloscope are a pair of parallel square metal plates carrying equal but opposite charges. The potential difference between the plates is 25.0 V Typical dimensions are about 3.3 cm on a side, with a separation of about 4.5 mm . The plates are close enough that we can ignore fringing at the ends. Part A Under these conditions. how much charge is on each plate? Part B How strong is the electric field between the plates? Part C If an electron is ejected at rest from the negative plates, how fast is it moving when it reaches the positive plate?

Explanation / Answer

*You have posted 2 different questions, so I will answer the first one.

A small sphere with mass 2.20 g hangs by a thread between two large parallel vertical plates 5.00 cm apart (Figure 1) . The plates are insulating and have uniform surface charge densities + and . The charge on the sphere is q = 7.70×106 C . Part A What potential difference between the plates will cause the thread to assume an angle of 30.0 with the vertical?

The force needed to keep the sting at angle 30° is given by
F = mg tan 30
= 2.2e-3* 9.8*tan30 =1.24477e-2 N

Electric field E = F/q = 1.24477e-2 / 7.7e6 =1.62e3 N/C

V = E*d = 1.62e3 *5e-2 = 81 V

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