3. A positively charged ion (charge +e; mass= 1.8x 10^-25kg) is accelerated thro

Question

3. A positively charged ion (charge +e; mass= 1.8x 10^-25kg) is accelerated through a voltage difference and undergoes the trajectory shown in the figure to right with d = 2.5 cm (please note that d is not a radius). The magnetic field is zero in the region where the ion is speeding up, and has d magnitude is 3.0 T elsewhere. You may assume that the ion loses negligible amounts of energy due to dissipative forces. a. In the region with non-zero magnetic field, is the field directed into the page or out of the page? Briefly explain your reasoning. b. Is the initial voltage, V, positive or negative? Briefly explain your reasoning. c. What is the voltage at the initial location of the ion?

Explanation / Answer

3)

a)

as the magnetic force , F = q * V X B

the magnetic field needed is OUT OF THE PAGE

b)

as the speed of the particle is increasing

for the positive charge ,

the plate Vi must be positive .

c)

as r = d/2

mass , m = 1.8 *10^-25 Kg

charge , q = 1.602 *10^-19 C

magnetic field , B = 0.3 T

the radius of the path is m

r = sqrt(2 * m * q * Vi)/(B*q)

0.025/2 = sqrt(2 *1.8*10^-25 *1.602 *10^-19 * Vi)/(3 * 1.602 *10^-19)

solving for Vi

Vi = 625.8 V

the initial potential at the position of particle is 625.8 V

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