Question

In: Physics

1. A doubly ionized particle of 17O (m = 2.822 x 10-26 kg) moves at a...

1. A doubly ionized particle of ¹⁷O (m = 2.822 x 10^-26 kg) moves at a speed of 5.680 x 10⁵ m/s through an 8.750 mT magnetic field, experiencing an acceleration of 4.370 x 10¹⁰ m/s².

(a) What is the magnitude of the centripetal force acting on the particle?

(b) What is the component of the velocity that moves the particle in a circular path?

(c) What is the angle that the velocity vector makes with the magnetic field vector?

(d) Does the particle move along the magnetic field? If so, at what speed?

(e) Elon Musk has decided that making solenoids would me much more lucrative than making electric cars, so that he wants to design and build a 1500-turn solenoid that runs on 2.750 A. What length does this solenoid need to produce the size magnetic field required for the ¹⁷O particle to move through?

Expert Solution

given :

m =

v =

B =

a =

q =

Now,

a) The centripetal force is provided by the magnetic force.

Therefore, Magnetic force = F = ma = [answer]

b) Magnetic force = F = [ = component of velocity perpendicular to magnetic field or component of velocity that moves the particle in circular path]

=> = F/qB = [answer]

d) The component of velocity along magnetic field is =

net velocity =

therefore,

c) the angle made by the velocity vector with magnetic field is

therefore, [answer]

e) we have the value of magnetic field B =

Magnetic field due to a solenoid = [N = no of turns, i = current , l = length]

the B should be equal to

therefore,

.

length of solenoid required is 0.59 m. [answer]

genius_generous answered 2 years ago

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