Question

An electron having mass 9.1 × 10–31 kg, charge 1.6 × 10–19 C and moving with the velocity of 10 6 m/s enters a region where magnetic field exists. If it describes a circle of radius 0.2 m then the intensity of magnetic field must be _× 10–5 T​

Answer 1

Answer:

An electron having a mass $9.1*10^{-31}kg$ , charge $1.6*10^{-19}C$, and moving with a velocity of $10^{6} m/s$ enters a region where a magnetic field exists. If it describes a circle of the radius $0.2m$ then the intensity of the magnetic field must be $2.8*10^{-5}T$

Explanation:

When a charged particle with charge $q$ is moving with a velocity $v$ enters a region where a magnetic field $B$ exists, it will experience a force called Lorentz magnetic force, It can be expressed as

$F_B=q\left(v\times B\right)$

Here the charged particle describes a circle, for this, the centripetal force is provided by Lorentz magnetic force

to get the value of the magnetic field we need to equate the two forces

$\begin{array}{l}F_B=F_C\\q\left(v\times B\right)=\frac{mv^2}{r}\end{array}$

so the magnetic field is

$\begin{array}{l}\\B=\frac{mv}{qr}\end{array}$

substituting  the given values we get, $B= \frac{9.1*10^{-31}*10^{6} }{1.6*10^{-19}*0.2 } =28.43*10^{-6} T$

$B=2.8*10^{-5}T$