Answer:
The acceleration of an electron is ![1.2\times10^{20}\ m/s^2](https://tex.z-dn.net/?f=1.2%5Ctimes10%5E%7B20%7D%5C%20m%2Fs%5E2)
Explanation:
Given that,
One Charge = 50 μC
Distance on y axis = 3.0 cm
Second charge = 77 μC
Distance on x axis = 4.0 cm
We need to calculate the force on electron due to q₁
Using formula of force
![F_{1}=\dfrac{kq_{1}q}{r^2}](https://tex.z-dn.net/?f=F_%7B1%7D%3D%5Cdfrac%7Bkq_%7B1%7Dq%7D%7Br%5E2%7D)
Here, q = charge of electron
Put the value into the formula
![F_{1}=\dfrac{9\times10^{9}\times50\times10^{-6}\times1.6\times10^{-19}}{(3\times10^{-2})^2}](https://tex.z-dn.net/?f=F_%7B1%7D%3D%5Cdfrac%7B9%5Ctimes10%5E%7B9%7D%5Ctimes50%5Ctimes10%5E%7B-6%7D%5Ctimes1.6%5Ctimes10%5E%7B-19%7D%7D%7B%283%5Ctimes10%5E%7B-2%7D%29%5E2%7D)
![F_{1}=8\times10^{-11}j\ \ N](https://tex.z-dn.net/?f=F_%7B1%7D%3D8%5Ctimes10%5E%7B-11%7Dj%5C%20%5C%20N)
We need to calculate the force on electron due to q₂
Using formula of force
![F_{2}=\dfrac{kq_{2}q}{r^2}](https://tex.z-dn.net/?f=F_%7B2%7D%3D%5Cdfrac%7Bkq_%7B2%7Dq%7D%7Br%5E2%7D)
Here, q = charge of electron
Put the value into the formula
![F_{2}=\dfrac{9\times10^{9}\times77\times10^{-6}\times1.6\times10^{-19}}{(4\times10^{-2})^2}](https://tex.z-dn.net/?f=F_%7B2%7D%3D%5Cdfrac%7B9%5Ctimes10%5E%7B9%7D%5Ctimes77%5Ctimes10%5E%7B-6%7D%5Ctimes1.6%5Ctimes10%5E%7B-19%7D%7D%7B%284%5Ctimes10%5E%7B-2%7D%29%5E2%7D)
![F_{2}=6.93\times10^{-11}i\ \ N](https://tex.z-dn.net/?f=F_%7B2%7D%3D6.93%5Ctimes10%5E%7B-11%7Di%5C%20%5C%20N)
We need to calculate the net force
Using formula of net force
![F=F_{1}+F_{2}](https://tex.z-dn.net/?f=F%3DF_%7B1%7D%2BF_%7B2%7D)
Put the value into the formula
![F=8\times10^{-11}j+6.93\times10^{-11}i](https://tex.z-dn.net/?f=F%3D8%5Ctimes10%5E%7B-11%7Dj%2B6.93%5Ctimes10%5E%7B-11%7Di)
The magnitude of the net force
![F=1.058\times10^{-10}\ N](https://tex.z-dn.net/?f=F%3D1.058%5Ctimes10%5E%7B-10%7D%5C%20N)
We need to calculate the acceleration of an electron
Using formula of force
![F = ma](https://tex.z-dn.net/?f=F%20%3D%20ma)
![a=\dfrac{F}{m}](https://tex.z-dn.net/?f=a%3D%5Cdfrac%7BF%7D%7Bm%7D)
Put the value into the formula
![a=\dfrac{1.058\times10^{-10}}{9.1\times10^{-31}}](https://tex.z-dn.net/?f=a%3D%5Cdfrac%7B1.058%5Ctimes10%5E%7B-10%7D%7D%7B9.1%5Ctimes10%5E%7B-31%7D%7D)
![a=1.2\times10^{20}\ m/s^2](https://tex.z-dn.net/?f=a%3D1.2%5Ctimes10%5E%7B20%7D%5C%20m%2Fs%5E2)
Hence, The acceleration of an electron is ![1.2\times10^{20}\ m/s^2](https://tex.z-dn.net/?f=1.2%5Ctimes10%5E%7B20%7D%5C%20m%2Fs%5E2)