The figure below shows a uniform magnetic field confined to a cylindrical volume

Question

                    The figure below shows a uniform magnetic field  confined to a                     cylindrical volume of radius R. The magnitude of  is decreasing                     at a constant rate of 10.2 mT/s.                 

                    What are (a) the x-component, (b) the y-component, and (c) the z-component of the initial acceleration of an electron                     released at point a (radial distance r = 6.70 cm)?                 

                    What are (d) the x-component, (e) the y-component, and (f) the z-component of the initial acceleration of an electron                     released at point b (r = 0 cm)?                 

                    What are (g) the x-component, (h) the y-component, and (i) the z-component of the initial acceleration of an electron                     released at point c (radial distance r = 6.70 cm)?                 

Explanation / Answer

a)

int{E.dl} = A dB/dt

==> E (2 pi r) = pi r^2 (dB/dt)

==> E = (r/2) (dB/dt)

==> E = (dB/dt)/2 r = 10.2e-3/2 = 0.0051 r

a = qE/m = 1.6e-19*0.0051*0.0670/9.109e-31 = 6.00 x 10^7 m/s2

==> ax = -6.00 x 10^7 m/s2

b)

ay = 0 m/s2

c)

az = 0 m/s2

d)

ax = 0 m/s2

e)

ay = 0 m/s2

f)

az = 0 m/s2

g)

ax = -6.00 x 10^7 m/s2

h)

ay = 0 m/s2

i)

az = 0 m/s2

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.