Question

An electron is rotating around an infinite positive linear charge in a circle of radius 0.1 m, if the linear charge density is 1μC/m, then the velocity of electron in m/s will be
A) 0.562×107
B) 5.62×107
C) 562×107
D) 0.0562×107

Answer 1

Hint:We know that both the magnetic and electric forces somehow influence the motion in a magnetic field. Although there will be a change in the trajectory of the particles in both the forces, the charged particle can be an ion or an atom with an electric charge. Below we will learn about the effects of the electric and magnetic force on a charged particle.

Complete step by step answer:
We will now express the condition for velocity of the electron when electrostatic force equals the centripetal force.
$v = \sqrt {\dfrac{{2kq\lambda }}{m}} $
Here, q is the charge on the electron, m is the mass of the electron, k is equal to $\dfrac{1}{{4\pi {\varepsilon _0}}}$ and $\lambda $ is the linear charge density.
We will now substitute the required values and we get,
$ \Rightarrow v = \sqrt {\dfrac{{2 \times 9 \times {{10}^9} \times 1.6 \times {{10}^{ - 19}}\,C \times {{10}^{ - 6}}}}{{9.1 \times {{10}^{ - 31}}\,kg}}} \\$
$ \Rightarrow v = 5.62 \times {10^7}\;m/s$

Therefore, the correct option is (B).

Additional Information:An atom consists of a positively charged nucleus at the centre with electrons revolving around it in closed orbits. The nucleus contains nucleons which are neutrons and protons. Neutrons have zero charge while protons are positively charged with the same charge as an electron. The electrons have very small mass compared to nucleons while nucleons are responsible for giving mass to an atom so all the mass of the atom is concentrated in the nucleus. The electrons are responsible for all the chemical properties of a substance while nucleons are responsible for nuclear properties like radioactivity, etc

Note:We know that the Gauss theorem gives an important corollary which states that the electric flux from any closed surface is due to the positive charges (sources) and negative charges (sinks) of the electric field enclosed by the surface. This means that no external charges contribute to the electric flux.