Question

An electron is moving with a speed of \[{10^8}m/sec\;\] perpendicular to a uniform magnetic field of intensity \[B\]. Suddenly the magnetic field is reduced to \[B/2\]. Find the radius of the path from the original value of \[r\].
A. No change
B. Reduced to \[r/2\]
C. Increases to \[2r\]
D. Stop moving

Answer 1

Hint: In the given question, we need to find the radius of the path from the original value of \[r\]. For this, we need to use the relation between the radius of the circular path for an electron in the magnetic field and the magnetic field to get the desired result.


Formula used:
The following formula is used for solving the given question.
The radius of the circular path for an electron in the magnetic field is inversely proportional to the magnetic field.
\[r\alpha \dfrac{1}{B}\]
Here, \[r\] is the radius and \[B\] is the magnetic field.





Complete answer:
We know that there is an inverse relation between the radius of the circular path for an electron in the magnetic field and the magnetic field.
Mathematically, it is given by
\[r\alpha \dfrac{1}{B}\]
Here, \[r\] is the radius and \[B\]is the magnetic field.
That means, \[\dfrac{{{r_1}}}{{{r_2}}} = \dfrac{{{B_2}}}{{{B_1}}}\]
This gives \[{r_2} = \dfrac{{{r_1} \times {B_1}}}{{{B_2}}}\]
Here, \[{r_1} = r\]and \[{B_2} = {B_1}/2\]
So, we get
\[{r_2} = \dfrac{{r \times {B_1}}}{{{B_1}/2}}\]
By simplifying, we get
\[{r_2} = 2r\]
Hence, the radius of the path from the original value of \[r\] is increased to \[2r\].
Therefore, the correct option is (C).





Note: Many students make mistakes in calculation as well as writing relation between radius of circular path for a particle in a magnetic field and magnetic field. This is the only way, through which we can solve the example in the simplest way. Also, it is essential to analyze the result of relation to get the desired result.