an electron moving with the speed of 1067 m/s is passed into a magnetic field of intensity 0.1T normally.what is the radius of the path of the electron inside the field? if the strength of the magnetic field is doubled, what is the new radius of the path? (e/m=108*10611 C/kg)

To find the radius of the path of the electron inside the magnetic field, we can use the formula for the radius of the circular path of a charged particle moving in a magnetic field:

r = (m * v) / (e * B)

Where:
r is the radius of the path
m is the mass of the electron
v is the velocity of the electron
e is the charge of the electron
B is the magnetic field strength

Given:
v = 1067 m/s
B = 0.1 T
e/m = 108 * 10^6 C/kg

First, let's calculate the mass of the electron:
m = e / (e/m)
= 1.6 * 10^-19 C / (108 * 10^6 C/kg)
= 1.6 * 10^-19 C / (108 * 10^6 C/(1kg/10^3g))
= (1.6 * 10^-19) * (10^3 / (108 * 10^6)) kg
= 1.6 * 10^-19 * (10^3 / 108) * 10^-6 kg
= 1.6 * (10^-19 * 10^-3 / 10^-6) / 108 kg
= 1.6 * (10^-19 * 10^-3 * 10^6 / 108) kg
= 1.6 * 10^-19 * 10^-3 * 10^6 / 108 kg
≈ 1.48148 * 10^-29 kg

Now substitute the values into the equation:

r = (m * v) / (e * B)
= (1.48148 * 10^-29 kg * 1067 m/s) / (1.6 * 10^-19 C * 0.1 T)
= (1.58148116 * 10^-26 kg m/s) / (0.16 * 10^-18 C T)
= (1.58148116 * 10^-26) / (0.16 * 10^-18) m/T
≈ 9.88271 * 10^-9 m/T

Therefore, the radius of the path of the electron inside the field is approximately 9.88271 * 10^-9 meters per Tesla (m/T).

Now, to find the new radius of the path when the strength of the magnetic field is doubled, we can use the same formula and substitute the new value of B:

New radius (r') = (m * v) / (e * B')

Where B' is the new magnetic field strength.

If the strength of the magnetic field is doubled, B' = 2 * B.

Substituting the known values:

New radius (r') = (1.48148 * 10^-29 kg * 1067 m/s) / (1.6 * 10^-19 C * (2 * 0.1) T)
= (1.58148116 * 10^-26) / (0.16 * 10^-18 * 2) m/T
= (1.58148116 * 10^-26) / (0.32 * 10^-18) m/T
≈ 4.94152 * 10^-9 m/T

Therefore, the new radius of the path when the strength of the magnetic field is doubled is approximately 4.94152 * 10^-9 meters per Tesla (m/T).