ks People Window Hup HW1-CH21 iew?offset-next&assignmentProblemID-80291960; prev

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ks People Window Hup HW1-CH21 iew?offset-next&assignmentProblemID-80291960; previous 4 of 10 next Part A If two electrons are each 1.60 10-10 on the proton. (Eigure 1) n from a proton, as shown in the figure, find the magnitude and of the net electrical force they will exert Submit My Answers Give Up Part B Find the direction of the net electrical force electrons will exert on the proton Enter your answer as an angle measured relative to the line connecting the proton and the right electron with counterclockwise being positive My Answers Give Up 40)

Explanation / Answer

Part(a): The two forces applied by the electron on the proton needs to be resolved as vectors.

So, Consider the two electrons as two vectors. Each vector is of the same size, and are attractive and are in different directions - 65° separation from each other.
The magnitude of each force vector can be calculated by the formula:-

F= k qQ/d²

Where,

f= force exerted on the proton

K= constant

q= charge of electron

Q=charge of proton

d= distance between the electron and proton

In this case both the electron and the proton have the same charge but opposite sign of 1.6x10^-19 C
the constant k = 9x10^9 Nm²C-²

F= k qQ/d²

After substituting the value for each variable,

F= k (1.6x10^-19)²/(1.6x10^-10)²
F= 9 x 10^-9 N

Now, the force will be resolved in two components i.e Vertical component and horizontal component.

Horizontal components:
Total Horizontal Force = Fh = F + Fcos65°
Fh = 9 x 10^-9 + 9 x 10^-9 x cos65° = 12.8 x 10^-9 N (horizontal component of force)

Vertical component is only due to the force at the angle:
Total Vertical force = Fv = F sin65°
Fv = 8.16x10^-9 (vertical component of force)
By using Pythagoras theorem, find the total force,
Total force = ((12.8 x 10^-9)² + (8.16x10^-9)²)
Total Force = 15.2 x 10^-9 N(ans)

Part (b): As both the electrons will have the same charge, therefore both electrons will attract the proton towards itself equally.

So equal force is applied on the proton by both the electrons. Since, The electrons have same charge and are separated from the proton at an equal distance, therefore the direction of the net force they exert on it is exactly halfway between the two rays from the proton to the two electrons.The direction is 32.5 degrees to the line connecting the proton to the right electron.

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