Question:
A proton with energy of 2 MeV enters a uniform
magnetic field of2.5 T normally. The magnetic force on
the proton is
(Take mass of proton to be $1.6 \times 10^{-27} kg )$
A proton with energy of 2 MeV enters a uniform
magnetic field of2.5 T normally. The magnetic force on
the proton is
(Take mass of proton to be $1.6 \times 10^{-27} kg )$
Updated On: Apr 15, 2024
- $3 \times 10^{-12}N$
- $8 \times 10^{-10}N$
- $8 \times 10^{-12}N$
- $2 \times 10^{-10}N$
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The Correct Option is C
Solution and Explanation
Energy of proton = 2 MeV
$\hspace15mm =2 \times 1.6\times10^{-19}\times10^6 J $
$\hspace15mm =3.2 \times 10^{-13}J$
Magnetic field (B)=2.5 T
Mass of proton (m) $=1.6 \times 10^{-27}kg$
Energy of proton $E= \frac {1}{2}mv^2$
$\therefore \hspace5mm v= \sqrt {\frac {2E}{m}} \hspace10mm ...(i) $
Magnetic force on proton
$\hspace15mm F=Bqv \, sin \, 90^\circ $
$\hspace15mm =Bqv$
Substituting the value of v from E (i)
$\hspace15mm F=Bq \sqrt {\frac {2E}{m}}$
$\hspace15mm =2.5 \times 1.6\times10^{-19} \sqrt {\frac {2\times3.2\times10^{-13}}{1.6 \times 10^{-27}}}$
$\hspace15mm =8 \times 10^{-12}N$
$\hspace15mm =2 \times 1.6\times10^{-19}\times10^6 J $
$\hspace15mm =3.2 \times 10^{-13}J$
Magnetic field (B)=2.5 T
Mass of proton (m) $=1.6 \times 10^{-27}kg$
Energy of proton $E= \frac {1}{2}mv^2$
$\therefore \hspace5mm v= \sqrt {\frac {2E}{m}} \hspace10mm ...(i) $
Magnetic force on proton
$\hspace15mm F=Bqv \, sin \, 90^\circ $
$\hspace15mm =Bqv$
Substituting the value of v from E (i)
$\hspace15mm F=Bq \sqrt {\frac {2E}{m}}$
$\hspace15mm =2.5 \times 1.6\times10^{-19} \sqrt {\frac {2\times3.2\times10^{-13}}{1.6 \times 10^{-27}}}$
$\hspace15mm =8 \times 10^{-12}N$
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Concepts Used:
Magnetic Field
The magnetic field is a field created by moving electric charges. It is a force field that exerts a force on materials such as iron when they are placed in its vicinity. Magnetic fields do not require a medium to propagate; they can even propagate in a vacuum. Magnetic field also referred to as a vector field, describes the magnetic influence on moving electric charges, magnetic materials, and electric currents.
A magnetic field can be presented in two ways.
- Magnetic Field Vector: The magnetic field is described mathematically as a vector field. This vector field can be plotted directly as a set of many vectors drawn on a grid. Each vector points in the direction that a compass would point and has length dependent on the strength of the magnetic force.
- Magnetic Field Lines: An alternative way to represent the information contained within a vector field is with the use of field lines. Here we dispense with the grid pattern and connect the vectors with smooth lines.
Properties of Magnetic Field Lines
- Magnetic field lines never cross each other
- The density of the field lines indicates the strength of the field
- Magnetic field lines always make closed-loops
- Magnetic field lines always emerge or start from the north pole and terminate at the south pole.