Helical Motion

Q. Which of the following particles will experience minimum magnetic force when projected with the same velocity perpendicular to magnetic field in the same magnetic field?

1. $\alpha -$particle
2. Proton
3. ${\text{Be}}^{3+}$
4. ${\text{Li}}^{2+}$

Q. The electric field lines for a system of two charges $Q_1$ and $Q_2$ fixed at two different points on the $\text{x-}$axis are as shown in the figure. Then $\frac{Q_1}{Q_2}$ might be

1. $\frac{9}{13}$
2. $\frac{13}{9}$
3. $1$
4. impossible to determine

Q. When a charged particle is projected at some angle in a magnetic field, the path attained will be

1. Parabola
2. Ellipse
3. Helical
4. Circle

Q. 47. Figure shows a system of point masses placed on X axis. Find the net gravitational field intensity at the origin.

Q. Two equal and opposite charges $q$ with a separation $2a$ form an electric dipole of dipole moment $p=\left(2qa\right)$. The line joining the midpoint of dipole to a point $R$ at a distance $r$ from it makes an angle $\theta$ with the dipole axis. The electric potential at $R$ (when $r>>a$) will be

1. $V=\frac{p\sin \theta }{4\pi {ϵ}_{0}r}$
2. $V=\frac{p\cos \theta }{4\pi {ϵ}_0{r}^2}$
3. $V=\frac{p\cos \theta }{4\pi {ϵ}_{0}r}$
4. $V=\frac{p\sin \theta }{4\pi {ϵ}_0{r}^2}$

Q. A positive charged particle enters in a magnetic field such that the component of its velocity along the field is 3 m/s and perpendicular to the field is 2 m/s. If the Time period of the particle to turn by $2\pi$ radians is 2 s, what will be its pitch?

1. 5 m
2. 6 m
3. 4 m
4. 8 m

Q. At a place, the earth's horizontal component of magnetic field is $0.38\times {10}^{-4}\text{T}$. If the angle of dip at that place is ${60}^{\circ }$, then the vertical component of earth's magnetic field at that place will be approximately -

1. $0.12\times {10}^{-4}\text{T}$
2. $0.24\times {10}^{-4}\text{T}$
3. $0.65\times {10}^{-4}\text{T}$
4. $0.40\times {10}^{-4}\text{T}$

Q. At a certain place the angle of dip is ${30}^{\circ }$ and the horizontal component of earth's magnetic field is $0.50\text{Oe}$. The earth's total magnetic field is (in Oestred)

1. $\sqrt{3}$
2. $1$
3. $\frac{1}{\sqrt{3}}$
4. $\frac{1}{2}$

Q.

A particle of specific charge $\alpha$ starts moving from the origin under the action of an electric field $\overrightarrow{E}=E_0\hat{i}$ and magnetic field $\overrightarrow{B}=B_0\hat{k}$. Its velocity at $(x_0,y_0,0)$ is $(4\hat{i}+3\hat{j})$. The value of $x_0$ is

1. $\frac{16\alpha B_0}{E_0}$

2. $\frac{13\alpha E_0}{2B_0}$

3. $\frac{25}{2\alpha E_0}$

4. $\frac{5\alpha }{2B_0}$

Q. what is the gravitational field intensity of a particle at the surface of the earth and at a point which is 10 km inside the earth?

Q. A charged particle is fired at an angle $\theta$ to a uniform magnetic field directed along the x-axis. During its motion along a helical path, the particle will

1. Never move parallel to the x-axis.
2. Move parallel to the x-axis once during every rotation for all values of $\theta$
3. Move parallel to the x-axis at least once during every rotation if $\theta ={45}^{\circ }$.
4. Never move perpendicular to the x-direction.

Q. A charged particle is fired at an angle $\theta$ to a uniform magnetic field directed along the x-axis. During its motion along a helical path, the particle will

1. Never move parallel to the x-axis.
2. Move parallel to the x-axis once during every rotation for all values of $\theta$
3. Move parallel to the x-axis at least once during every rotation if $\theta ={45}^{\circ }$.
4. Never move perpendicular to the x-direction.

Q. Uniform electric and magnetic fields with strength E and induction B, respectively, are along $y$ -axis as shown in the figure. A particle with specific charge $q/m$ leaves the origin 0 in the direction of $x$ -axis with an initial non relativistic velocity $v_0.$ The coordinate $y_n$ of the particle when it crosses the $y$ -axis for the $n^{\text{th}}$ time is

1. $\frac{2{\pi }^{2}m{n}^{2}E}{q{B}^2}$
2. $\frac{{\pi }^{2}m{n}^{2}E}{q{B}^2}$
3. $\frac{{\pi }^{2}m{n}^{2}E}{3q{B}^2}$
4. $\frac{\sqrt{3}p{i}^{2}m{n}^{2}E}{q{B}^2}$

Q. A charged particle is fired at an angle $\theta$ to a uniform magnetic field directed along the $x–$axis. During its motion along a helical path, if the pitch of the helical path is equal to the maximum distance of the particle from the $x–$ axis, then

1. $\cos \theta =\frac{1}{\pi }$
2. $\sin \theta =\frac{1}{\pi }$
3. $\tan \theta =\frac{1}{\pi }$
4. $\tan \theta =\pi$