Electrons in Earth's upper atmosphere have typical speeds near 5.87 ✕ 105 m/s. HINT (a) Calculate the magnitude of Earth's magnetic field if an electron's velocity is perpendicular to the magnetic field and its circular path has a radius of 6.81 ✕ 10−2 m. T (b) Calculate the number of times per second that an electron circles around a magnetic field line.

a) 4.8×10^-5T

b) 7.38×10^-7seconds

Explanation:

The centripetal force in a magnetic field is given by:

qvB= mv2/r

Where q= charge of the ion

m= mass of the ion

r= radius of the circular path

B= magnetic field

V= velocity

Rearranging to make B subject of formular gives:

B=mv/r

B= [(9.11×10^-31)×(5.87×10^5)]/ [(1.6×10^-19)×(6.81×10^-2)]

B = (5 34×10^-25)/(1.099×10^-20)

B= 4.86×10^-5T

b) T =( 2 pi × r)/v

T = 2 × 3.142 x (6.81×10^-2) / (5.87×10^5

T = 0.428/ (5.87×10^5)

T = 7.38 × 10^-7seconds

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation:

it is the second option.