Question

An electron is to be released from rest on the central axis of a uniformly charged disk of radius R. The surface charge density on the disk is +4.00 μC/m^2 and ε0= 8.85 x 10^–12 F/m. What is the magnitude of the electron’s initial acceleration if released at distances of

a. R from the center of the disk?
b. R/100 from the center of the disk?
c. R/1000 from the center of the disk?
d. Why does the acceleration increase only slightly as the release point is moved closer to the disk?

Answer 1

Answer:

$a=11.86*10^1^5 m/s$

$a=3.91864074*10^-^2^4 m/s^2$

$a=3.95426275*10^-^2^4m/s^2$

Explanation:

From the question we are told that

The surface charge density on the disk is $\sigma=+4.00 \mu C/m^2$

$\varepsilon _0= 8.85 * 10^–12 F/m.$

a)Generally the electric field in this situation is given as  is mathematically given as

  $E=\frac{\sigma}{\varepsilon_0} (1-\frac{R}{\sqrt{2}R}$

  $E=\frac{\sigma}{\varepsilon_0} (1-\frac{1}{\sqrt{2}})$

  $E=67.48*10^3 f/a$

Generally the Force of release of the electron  is mathematically given as

$F=eE$

$F=ma$

$a*m=\frac{eE}{1}$

$a=\frac{1.6*10^-^1^9 *67.48*10^3}{9.1*10^3^1}$

$a=11.86*10^1^5 m/s$

b)Generally the electric field in R/100 from the center of the disk is given as  is mathematically given as

Generally

 $E=\frac{\sigma}{\alpha \varepsilon_0}(1-\frac{1}{\sqrt{(100)^2} }$

 $E=\frac{4.0*10^-^6}{2*8.854*10^-^1^2}(1-\frac{1}{\sqrt{(1+(100)^2} })$

 $E=2.22872692*10^2^7$

Generally the Force of release of the electron  is mathematically given as

 $a*m=\frac{eE}{1}$

 $a=\frac{1.6*10^-^1^9 *2.22872692*10^2^7}{9.1*10^3^1}$

 $a=3.91864074*10^-^2^4 m/s^2$

c)Generally the electric field in R/1000 from the center of the disk is given as  is mathematically given as

 $E=\frac{\sigma}{\alpha \varepsilon_0}(1-\frac{1}{\sqrt{(1000)^2} }$

 $E=\frac{4.0*10^-^6}{2*8.854*10^-^1^2}(1-\frac{1}{\sqrt{(1+(1000)^2} })$

$E=2.24898694*10^2^7$

Generally the Force of release of the electron  is mathematically given as

 $a*m=\frac{eE}{1}$

 $a=\frac{1.6*10^-^1^9 *2.24898694*10^2^7}{9.1*10^3^1}$

 $a=3.95426275*10^-^2^4m/s^2$