Voltage and charge question?

2016-07-30 12:16 pm

A small ball (radius 1.5cm) is coated with a metallic paint and charged by an EHT at 2kV What is the charge q on the ball?

The ball is hung by a piece of thread in the space between two oppositely charged parallel plates. The thread makes an angle of 15 with the vertical (Fig 18.55). The mass of the ball is 0.5 g.Find the electric field intensity between the two plates.

Please help me I don't even know how to start part a how can a ball charge by an EHT

回答 (1)

天同

2016-07-31 10:26 am

✔ 最佳答案

When a ball is charged by using an EHT, the ball will acquire the same potential as that provided by the EHT.

Since potential of a spherical object = kq/r
where k is the electrostatic constant (= 9 x 10^9 F/m)
q is the charge on the object with radius r

hence, 2000 = (9 x 10^9)q/(0.015)
i.e. q = 3.33 x 10^-9 C
-------------
Let T be the tension in the thread. Resolve T horizontally and vertically, we have:
Horizontally, T.sin(15) = qE -------- (1)
where E is the electric field intensity between the plates
Vertically, T.cos(15) = mg ------------- (2)
where m is the mass of the ball (= 0.5 x 10^-3 kg)
g is the acceleration due to gravity (= 9.81 m/s^2)

(1)/(2): sin(15)/cos(15) = qE/mg
i.e. E = (mg/q).tan(15) = [(0.5x10^-3).(9.81)/(3.33 x 10^-9)].tan(15) v/m
E = 3.95 x 10^5 v/m

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