A small object with mass m, charge q, and initial speed v 0 = 5.00×10 3 m/s is p

Question

A small object with mass m, charge q, and initial speed v0 = 5.00×103 m/s is projected into a uniform electric field between two parallel metal plates of length 26.0 cm (Figure 1) . The electric field between the plates is directed downward and has magnitude E = 800 N/C . Assume that the field is zero outside the region between the plates. The separation between the plates is large enough for the object to pass between the plates without hitting the lower plate. After passing through the field region, the object is deflected downward a vertical distance d = 1.25 cm from its original direction of motion and reaches a collecting plate that is 56.0 cm from the edge of the parallel plates. Ignore gravity and air resistance.

Calculate the object's charge-to-mass ratio, q/m.

Explanation / Answer

Force on object

F= qE

F =ma

a = q/m E

let q/m = k

a = kE = k800

now for horizontal motion of 26cm time taken

t1 = 0.26/v = 0.000052 sec

for vertical motion for t1 sec

S = 0.5axt1^2

S = 0.000001081k

Now for remaining 56 cm time taken t2

t2 = 0.56/v = 0.000112sec

Now for t2 sec vertical motion

S2 = (at1) t2

S2 = 0.000004659 k

given d = S+S2

0.0125 = s+S2

k = 2177.62

q/m = 2177.62

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