Q.46

Expert-verifiedFound in: Page 711

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

Proton moves along the x-axis where some arrangement of charges has produced the potential , where and l = 1.0 mm.

a. What minimum speed must the proton have at x = 0 to move down the axis without being reflected?

b. What is the maximum speed reached by a proton that at x = 0

a)The minimum Speed of Proton is equal to

b)The minimum Speed of Proton is equal to

As per the energy conservation law energy neither can be created nor it can be destroyed.

Hence it can be said that the total energy under a preserved system cannot be changed.

Hence the charge system of electric filed can be writing as follows;

Here in this V are potential , v is the proton velocity and K is the Kinetic energy . Suffix i denotes initial Stage, and f denotes Final stage

a)

As the initial Potential Difference and the initial velocity of the particle is zero thus the equation can be written as;

now in this scenario,

maximum value of is Vo, thus this above equation can be written as;

.....eq.1

as per given Data Vo=5000 V and

the Mass and charge of proton are

Substituting the parameters of the equation with the data it can be shown as;

Hence;

a)The minimum Speed of Proton is equal to at x = 0 to move down the axis without being reflected

in b)

The portan can have maximum speed through potential function.

At this scenario the speed of proton at x = 0 is 9.8*10^6 m/s.

The potential bottom of this function will be then V= 10000 V .

Substituting these data with the equation part a can be shown as follows;

The maximum speed reached by a proton that is

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