91Ó°ÊÓ

The electrostatic force on the proton can be calculated using equation (1.1).

Rearranging equation (1.1) in order to get an expression for the electrostatic force.

\[F = qE\]

Here, \[q\] is the charge on proton \[\left( {q = 1.6 \times {{10}^{ - 19}}{\rm{ C}}} \right)\], and \[E\] is the intensity of the electric field \[\left( {E = 5.00 \times {{10}^6}{\rm{ N/C}}} \right)\]

The electrostatic force on the proton produces acceleration in the proton. The force on the proton is,

F = ma

Here, m is the mass of the proton \[\left( {m = 1.67 \times {{10}^{ - 27}}{\rm{ kg}}} \right)\], and a is the acceleration of the proton.

The expression for the acceleration of the proton is,

\[a = \frac{F}{m}\]

Using equation (1.2),

\[a = \frac{{qE}}{m}\]

Substituting all known values,

\begin{aligned} a &= \frac{{\left( {1.6 \times {{10}^{ - 19}}{\rm{ C}}} \right) \times \left( {5.00 \times {{10}^6}{\rm{ N/C}}} \right)}}{{\left( {1.67 \times {{10}^{ - 27}}{\rm{ kg}}} \right)}}\\ &= 4.79 \times {10^{14}}{\rm{ m/}}{{\rm{s}}^{\rm{2}}} \end{aligned}

Hence, the initial acceleration of the proton is \[4.79 \times {10^{14}}{\rm{ m/}}{{\rm{s}}^{\rm{2}}}\].