Assume the region to the right of a certain plane contains a uniform magnetic fi

Question

Assume the region to the right of a certain plane contains a uniform magnetic field of magnitude b = 1.85 mT and the field is zero in the region to the left of the plane as shown in the figure below. An electron, originally traveling perpendicular to the boundary plane, passes into the region of the field.

a) Determine the time interval required for the electron to leave the "field-filled" region, noting that the electron's path is a semicircle.

__________ S

(b) Assuming the maximum depth of penetration into the field is 2.29 cm, find the kinetic energy of the electron.
__________eV

Explanation / Answer

Here ,

magnetic field , B = 1.85 mT

a)

as the time period of the particle is given as

T = 2*pi*m/(B*q)

for travelling half circle

time taken = pi*m/(B*q)

time taken = pi * 9.11 *10^-31/( 0.00185 * 1.602 *10^-19)

time taken = 9.66 *10^-9 s

the time taken for the electron to come out is 9.66 *10^-9 s

b)

as the radius of electron is maximum penetration depth

r = 2.29 cm

let the kinetic energy is KE

r = sqrt( 2 * m * KE* e)/(B*e)

0.0229 = sqrt(2 * 9.11 *10^-31 * KE * 1.602 *10^-19)/(( 0.00185 * 1.602 *10^-19))

solving for KE

KE = 157.1 eV

the kinetic energy of electron is 157.1 eV

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects