Answer
Verified
319.6k+ views
Hint: Students should remember the equation of electric field E and the equation of kinetic energy in the form of linear momentum. Along with these Newton’s all three laws of motion are very important for the questions in which objects falling from a particular height for a particular time.
Complete step-by-step answer:
We know the equation of force,
\[F = q \times E\] …..(1)
and kinetic energy,
\[KE = \dfrac{{{p^2}}}{{2m}}\] …..(2)
Now, using Newton’s law we can write,
\[F = \dfrac{{dp}}{{dt}}\] …..(3)
By equating equations (1) and (3), we get
\[\dfrac{{dp}}{{dt}} = q \times E\]
\[dp = q \times Edt\]
On integrating above equation,
\[\int {dp} = \int\limits_0^t q \times Edt\]
\[p = qEt\] …..(4)
Squaring and adding equation (4) in equation (2) we get,
\[KE = \dfrac{{{q^2}{E^2}{t^2}}}{{2m}}\]
is a required solution.
Hence, a charged particle of mass m and charge q is released from rest in an electric field of uniform strength E. The kinetic energy of the particle after a time t will be
\[KE = \dfrac{{{q^2}{E^2}{t^2}}}{{2m}}\]
The correct option is C.
Note: Students should remember the formulae of force and kinetic energy in different forms. The integration and derivatives of basic functions are necessary in physics to solve problems containing dynamic functions.
Complete step-by-step answer:
We know the equation of force,
\[F = q \times E\] …..(1)
and kinetic energy,
\[KE = \dfrac{{{p^2}}}{{2m}}\] …..(2)
Now, using Newton’s law we can write,
\[F = \dfrac{{dp}}{{dt}}\] …..(3)
By equating equations (1) and (3), we get
\[\dfrac{{dp}}{{dt}} = q \times E\]
\[dp = q \times Edt\]
On integrating above equation,
\[\int {dp} = \int\limits_0^t q \times Edt\]
\[p = qEt\] …..(4)
Squaring and adding equation (4) in equation (2) we get,
\[KE = \dfrac{{{q^2}{E^2}{t^2}}}{{2m}}\]
is a required solution.
Hence, a charged particle of mass m and charge q is released from rest in an electric field of uniform strength E. The kinetic energy of the particle after a time t will be
\[KE = \dfrac{{{q^2}{E^2}{t^2}}}{{2m}}\]
The correct option is C.
Note: Students should remember the formulae of force and kinetic energy in different forms. The integration and derivatives of basic functions are necessary in physics to solve problems containing dynamic functions.
Recently Updated Pages
Basicity of sulphurous acid and sulphuric acid are
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
The branch of science which deals with nature and natural class 10 physics CBSE
What is the stopping potential when the metal with class 12 physics JEE_Main
The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Select the correct plural noun from the given singular class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
The sum of three consecutive multiples of 11 is 363 class 7 maths CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
How many squares are there in a chess board A 1296 class 11 maths CBSE