Solution:

Ans. Try yourself, Similar to Q. 3 (b) of Short Answer.

[AI Q. 7. (i) Write the expression for the magnetic force acting on a charged particle moving with velocity $v$ in the presence of magnetic field $B$.

(ii) A neutron, an electron and an alpha particle moving with equal velocities, enter a uniform magnetic field going into the plane of the paper as shown. Trace their paths in the field and justify your answer.

U [Dehhi, II, III 2016]

Ans.

(i)

(Give Full credit of this part even if a student writes :

$$ F=q v B \sin \theta $$

and force $(\vec{F})$ acts perpendicular to the plane containing $\vec{v}$ and $\vec{B}$ )

(ii)

$$ 1 / 2+1 / 2+1 / 2 $$

$\alpha$

n

$$ \xrightarrow{x} x \quad x \quad x $$

Justification : Direction of force experienced by the particle will be according to the Fleming’s left hand rule/(any other alternative correct rule.) 1/2

[CBSE Marking Scheme 2016]

Detailed Answer :

(i) A charged particle with charge $q$, moving with velocity $\vec{v}$, in a magnetic field having field strength $\vec{B}$, then the forceacting on it is given as :

$$ \begin{aligned} & \vec{F}=q(\vec{v} \times \vec{B}) \ & \vec{F}=\vec{F} q v B \sin \theta \hat{n} \end{aligned} $$

where, $\theta=$ angle between velocity and magnetic field

Here direction of force is shown by cross product of

(ii) velocity and ${\underset{x}{x}}^{x_{x}}{ }_{x}$.

Here, $\alpha$-particle will trace the circular path in a clockwise direction, since its deviation is in the direction of $\vec{v} \times \vec{B}$.

$1 / 2$

Neutron will pass without any deviation, as magnetic field, exerts no force on neutral particle. $1 / 2$ Electron will trace circular path in an anticlockwise direction, since its deviation is opposite to $\vec{v} \times \vec{B}$ with radius $r=\frac{m v}{q B}$.

$1 / 2$

It is further observed that the direction of force experienced by the particle will be as per Fleming’s left hand rule.