Question

1. An electron is projected with a velocity of 10 5 ms at right
angle to a magnetic field of 0.019 G . Calculate the radius
of the circle described by the election. given
e= 1.6×10 –19 C
Me = 9.1 × 10 -13 kg
​

Answer 1

Answer:

This question is a case of finding the radius of an electron in an uniform magnetic field. For an electron moving in a circular path, the centripetal force acting on it must be equal to the magnetic force faced by the electron.

$\implies F_c = F_m\\\\\\\implies \dfrac{mv^2}{r} = q\times v\times B\\\\\\\text{Cancelling 'v' from the RHS and LHS we get:}\\\\\\\implies \dfrac{mv}{r} = q \times B\\\\\\\implies \boxed{ \bf{ r = \dfrac{mv}{qB} }}$

According to the question,

• m = 9.1 × 10⁻³¹ kg
• v = 10⁵ m/s
• B = 0.019 G
• q = 1.6 × 10⁻¹⁹ C

Converting Magnetic field from Gauss to Tesla, we get:

⇒ 1 G = 10⁻⁴ T

⇒ 0.019 G = 1.9 × 10⁻² × 10⁻⁴ = 1.9 × 10⁻⁶ T

Substituting the values we get:

$\implies r = \dfrac{ 9.1 \times 10^{-31} \times 10^5}{1.6 \times 10^{-19} \times 1.9 \times 10^{-6}}\\\\\\\implies r = \dfrac{9.1 \times 10^{-26}}{ 3.04 \times 10^{-25}}\\\\\\\implies r = 2.99 \times 10^{-26+25}\\\\\\\implies r = 2.99 \times 10^{-1} \\\\\implies \boxed{ \bf{ r= 0.299\:\:m\:\:(or)\:\:29.9\:\:cm}}$

Therefore the radius of the electron is 29.9 cm.

Answer 2

Answer:

Given :-

An electron is projected with a velocity of 10⁵ m/s at right angle to a magnetic field of 0.019 G

To Find :-

Radius

Solution :-

We know that

Radius = Mass × Velocity/Magnetic Field × e

Radius = $\sf \dfrac{9.1 \times 10^{-31} \times 10^{5}}{1.6 \times 10^{-19} \times 1.9 \times 10^{-6}}$

Radius = $\sf \dfrac{9.2 \times 10^{(-31 + 5)}}{1.6 \times 1.9 \times 10^{-19 +(-6)}}$

Radius = $\sf \dfrac{9.2\times 10^{-26}}{3.04 \times 10^{-25}}$

Radius = $\sf \dfrac{9.2 \times 10^{-26 + 25}}{3.04}$

Radius = $\sf \dfrac{9.2\times 10^{-1}}{3.04}$

Radius = $\sf 2.99 \times 10^{-1}$

Radius = 29.9 cm