A particle with negative charge q and mass m = 2.50×10 15 kg is traveling throug

Question

A particle with negative charge q and mass m = 2.50×1015 kg is traveling through a region containing a uniform magnetic field B =(0.110T)k^. At a particular instant of time the velocity of the particle is v =(1.20×106m/s)(3i^+4j^+12k^)and the force F  on the particle has a magnitude of 2.45 N .

Part A

Determine the charge q.

Part B

Determine the acceleration a  of the particle. Find the x-component.

Part C

Find the y-component.

Part D

Find the z-component.

Part F

Determine the radius of curvature R of the circular component of the helical path.

Part G

Determine the cyclotron frequency of the particle.

There are three more questions after solving those problems.

Explanation / Answer

v = (2.10x 10^6 ) (-3i + 4j + 12k) m/s

B = (-0.110 T) k

A) magenetic force on particle,

Fm = q( v x B)

   = q[ ((2.10x 10^6 ) (-3i + 4j + 12k)) X (-0.110 k) ]

   = q(2.10 x 10^6) (-0.33j - 0.44i)

|F| = q(2.10 x 10^6)sqrt(0.33^2 + 0.44^2) = 2.45

q = 2.12 x 10^-6 C

B) a = Fm / m = [ (2.12 x 10^-6)(2.10 x 10^6) (-0.33j - 0.44i)]/(2.50 x 10^-15)

= (-7.84i -5.88j) x 10^14 m/s^2

x = -7.84 x 10^14 m/s^2

C) y = -5.88 x 10^14 m/s^2

D) z = 0

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