A calcium-40 ion has a positive charge that is double the charge of a proton, and a mass of 6.64 ✕ 10−26 kg. At a particular instant, it is moving with a speed of 5.05 ✕ 106 m/s through a magnetic field. At this instant, its velocity makes an angle of 64° with the direction of the magnetic field at the ion's location. The magnitude of the field is 0.170 T. (a) What is the magnitude of the magnetic force (in N) on the ion? (b) What is the magnitude of the ion's acceleration (in m/s2) at this instant?

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A calcium-40 ion has a positive charge that is double the charge of a proton, and a mass of 6.64 ✕ 10−26 kg. At a particular instant, it is moving with a speed of 5.05 ✕ 106 m/s through a magnetic field. At this instant, its velocity makes an angle of 64° with the direction of the magnetic field at the ion's location. The magnitude of the field is 0.170 T.
(a)
What is the magnitude of the magnetic force (in N) on the ion?
 
(b)
What is the magnitude of the ion's acceleration (in m/s2) at this instant?
Expert Solution
Step 1

Given:

The charge on the calcium 40 ion is +2e.

(e=1.6×10-19 C is the charge of the electron).

The mass of the calcium ion is m=6.64×10-26 kg.

The speed of the ion moving at any instant is v=5.05×106 ms.

Angle made with the direction of magnetic field is θ=640.

The magnitude of the magnetic field is B=0.17 T.

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