Electric charges and fields

 

Electric Charges and Fields

  
 Problems

Question1. Three-point charges of +2 μC, -3 μC, and -3 μC are kept at the vertices A, B, and C respectively of an equilateral triangle of the side of 20 cm as shown in the figure (a). What should be the sign and magnitude of the charge to be placed at the mid-point (M) of side BC so that the charge at A remains in equilibrium?



Question2. Calculate the electric field strength required to just support a water drop of mass 10-3 kg and having a charge of 1.6 × 10-19 C.

Solution. Here m = 10-3 kg, q = 1.6 × 10-19 C

Let E be the strength of the electric field required to just support the water drop. Then

Force on water drop due to electric field = Weight of water drop

Or                                  qE = mg

Question3. Calculate the voltage needed to balance an oil drop carrying 10 electrons when located between the plates of a capacitor which are 5 mm apart. The mass of oil drop is 3 × 10-16 kg. Take g = 10 ms-2.


Question4. How many electrons should be removed from a coin of mass 1.6 g, so that it may just float in an electric field of intensity 109 NC-1, directed upward?

Solution. Here m = 1.6 g = 1.6 × 10-3 kg,

                                                 E = 109 NC-1

Let n be the number of electrons removed from the coin,

Then charge on the coin,

                                                 q = + ne

When the coin just floats,

Upward force of electric field = Weight of coin

Or                                       qE      or      neE = mg

Question5. A pendulum of mass 80 milligrams carrying a charge of 2 × 10-8 C is at rest in a horizontal uniform electric field of 2 × 104 Vm-1. Find the tension in the thread of the pendulum and the angle it makes with the vertical.

Solution. Here m = 80 mg = 80 × 10-6 kg

        q = 2 × 10-8 C, E = 2 × 104 Vm-1



Question6. An electron moves a distance of 6 cm when accelerated from rest by an electric field of strength 2 × 104 NC-1. Calculate the time of travel. The mass and charge of the electron are 9 × 10-19 kg and 1.6 × 10-19 C respectively.

Solution. Force exerted on the electron by the electric field,

 


  Question7. An electron falls through a distance of 1.5 cm in a uniform electric field of magnitude 2.0 × 104 NC-1. Given in figure (a), the direction of the field is reversed keeping its magnitude unchanged and a proton falls through the same distance. Given in figure (b), compute the time of falls in each case. Contrast the situation (a) with that of ‘free fall under the gravity’.



Thus the heavier particle takes a greater time to fall through the same distance. This is in contrast to the situation of ‘free fall under gravity’ where the time of fall is independent of the mass of the body. Here the acceleration due to gravity ‘g’ being negligibly small has been ignored.


Question10. An electric field E is set up between the two parallel plates of a capacitor, as shown in the figure, an electron enters the field symmetrically between the plates with a speed v0. The length of each plate l. find the angle of deviation of the path of the electron as it comes out of the field.







                                  












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