An ion of mass m and charge of known magnitude q is observed to move in a straig

Question

An ion of mass m and charge of known magnitude q is observed to move in a straight line through a region of space in which a uniform magnetic field B points out of the paper and a uniform electric field E points toward the top edge of the paper, as shown in region I above. The particle travels into region II in which the same magnetic field is present, but the electric field is zero. In region II the ion moves m a circular path as shown. Indicate on the diagram at right the direction of the force on the ion at point P2 in region II. Is the ion positively or negatively charged? Explain clearly the reasoning on which you base your conclusion. Indicate and label clearly on the diagram at right the forces which act on the ion at point P1 in region I. Find an expression for the ion's speed v at point P1 in terms of E and B.

Explanation / Answer

(a) When we draw a tengent at the point P2 in the region II it gives the direction of the magnetic force acting on the charged particle due to the magnetic field which is shown in the below figure: (b) Sign of the charged particles is positive basing on the Fleming's left hand rule (c) At the point P1, Electric force acting on the charged particles due to presence of electric field is Fe = Eq Magnetic force acting on the charged particles due to the presence of electric is Fm = Bqv (d) If both these forces are equal then the particles wont deflect and travel in a straight line. Hence,   Eq = Bqv                E = Bv                 v = E / B

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