Q.46

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Found in: Page 711

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

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

See the step by step solution

## Step 1: Conservation of Energy

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

## Step 2: Application of Given data

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