Problem 21.78 Part A A small object with mass m, charge q, and initial speed Up

Question

Problem 21.78 Part A A small object with mass m, charge q, and initial speed Up = 6.00x103 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 600 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 = 1.35 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 g/ml = C/kg Submit Previous Answers Request Answer X Incorrect; Try Again Figure 1of1 Provide Feedback 26.0 cm 56.0 cm

Explanation / Answer

First of all determine the time taken by the object to cross the the plate -

This is -
t = d / v = 0.260m / (6.0x10^3) m/s = 4.33 x 10^-5 s

In order to have deflected as it did,
acceleration a = 2s / t² = 2 * 0.0135m / (4.33 x 10^-5 s)² = 1.44 x 10^7 m/s²

Now,

The electric field causes an electric force F = qE = ma,

Therefore, a = qE/m = (q/m) * E

=> q/m = a / E = (1.44 x 10^7) / (600) = 2.40 x 10^4 C/kg.

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