Question

Field and force with three charges At a particular moment, one negative and two positive charges are located as shown in the figure. Your answers to each part of this problem should be vectors. It helps a great deal to make a diagram with arrows representing the various electric field contributions, and then check the signs of your components against these arrows. 01 0 (a) Find the electric field at the location of Q1, due to Q2 and Q3 E-<-2.16e5, - 2.88e50> x N/C (b) Use the electric field you calculated in part (a) to find the force on Q1 (c) Find the electric field at location A, due to all three charges. N/C (d) An alpha particle (He2+, containing two protons and two neutrons) is released from rest at location A. Use your answer from part (c) to determine the initial acceleration of the alpha particle. (Use 6.646 x 1027 kg for the mass of He2+.) m/s2

Answer 1

Electric field due to a point charge Q at a distance r is given by

$E=$

In vector notation,

  

Where, is vector starting from the charge and ending to the point (where electric field is to be calculated). and

Given,  

  

(a) The electric field due to charge $Q_{2}$ and $Q_{3}$ at the location of $Q_{1}$ is shown below

Here, and is electric field due to charge $Q_{3}$ and $Q_{2}$ respectively. And

  

The magnitude of these electric fields can be calculated as

ー=337.5 x 105 N/C 4 x 10-2)2

The direction of this electric field is towards the positive y - direction. So,

And

  

   (only the magnitude because direction is already shown in the diagram)

72 x 105 N/C

In vector form can be written as

or,   

or,

So, net electric field due to charge $Q_{2}$ and $Q_{3}$ at the location of $Q_{1}$ is

  

   (in N/m)

(279.9 x 105) j+ (43.2x 105) ;

(b) So, the net force on $Q_{1}$ due to these two charges is

  

(c)  

OA 2 Nous So, net electric lidd at A OA net (423.6 x1o5)个t (60.3x(os)

(d)

Total charge on alpha particle = 2e = 2 x 1.602 x 10^-19 C = 3.204 x 10^-19 C

And total mass of alpha particle = 6.646 x 10^-27 kg

So, total force on the alpha particle at A is

(in N)

The acceleration of the alpha particle is

(2.07 x 105(0.3 x 1015)j

For any doubt please comment and please give an up vote. Thank you.