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A beam of protons (proton mass is 1.67 x 10 -​ 27 kg) moves at 3...

A beam of protons (proton mass is 1.67 x 10 -​ 27 kg) moves at 3 x 10 5​ m/s through a uniform magnetic field with magnitude 2 T. The magnetic field has exactly equal components along the positive ​y and negative ​x axes and no component along the ​z axis. The velocity of each proton lies in the ​xz-​ plane at an angle of 30 0​ ​to the​ z-​ axis.

(a) Write the magnetic field ​B and the velocity ​v of the proton in terms of their components using unit vectors ​i​, ​j​ & ​k.

(b) What is the ‘magnetic force’ experienced by each proton, expressed as a vector using unit vectors ​i​, ​j​ & ​k​?

(c) What are the magnitude and direction of the proton’s acceleration expressed as a vector using unit vectors ​i​, ​j​ & ​k​?

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