Question

An electron moving horizontally with a velocity of $4 \times {10^4}m/s$ enters a region of uniform magnetic field of ${10^{ - 5}}$T acting vertically downward as shown in figure. Draw its trajectory and find out the time it takes to come out of the region of the magnetic field.

Answer 1

Hint: The right hand rule is used to find the direction of the magnetic field due to the current element. If the thumb of the right hand is in the direction of current flow the curve finger shows the direction of the magnetic field. In mathematics and physics, the right-hand is a common mnemonic for understanding orientation of axes in three dimensional space. Most of the various left-and-right-hand rules arise from the fact that the three axes of three dimensional space have two possible orientations.

Complete step by step answer:
Time taken to cover complete circle,
$T = \dfrac{{2\pi }}{\omega } = \dfrac{{2\pi }}{{\left( {qB/m} \right)}}$
Here, T is time period, $\omega $is acceleration M is mass, B is magnetic field. the e/m value of the electron is $1.76 \times {10^{11}}$.
Time taken to cover semicircle,

$\dfrac{T}{2} = \dfrac{{m\pi }}{{qB}}$
$ = \dfrac{{3.14}}{{1.76 \times {{10}^{11}} \times {{10}^{ - 5}}}}$
$ = 1.78 \times {10^{ - 6}}\sec $
Therefore, time taken to cover a semicircle is $1.78\mu \sec $.

Note:
A magnetic field is a vector field. The magnetic field describes the magnetic influence on moving electric charges, electric current and any magnetized material. In physical terms it is a field that passes through space and which makes magnetic force move electric charges and magnetic dipole. In humans every organ and cell has its own magnetic field. This includes neurons, endocrine and muscle cells. Starting magnetic field affects implanted metallic devices such as pacemakers present insight to the body and has direct health consequently. A pacemaker is a small, battery-operated device. This device senses when your heart is beating irregularly or too slowly. It sends a signal to your heart that makes your heart beat at the correct pace. A pacemaker is insertion is the implantation of a small electronic device that is usually placed in the chest (just below the collarbone) to help regulate slow electrical problems with the heart.