An infinite long thin straight wire carries a current which increases linearly with time. A point positive test charge is released at point 'p' close to the wire as shown in the figure.

To which of the following quantities, the radius of the circular path of a charged particle moving at right angles to a uniform magnetic field is directly proportional?

Two parallel metal plates $A$ and $B$ separated by a distance $25 \mathrm{cm}$ are connected to an ammeter. Photons of energy $3.28 \mathrm{eV}$ are incident on the photosensitive plate $A$ of threshold wavelength $5000 \stackrel{\mathrm{o}}{\mathrm{A}}$. The minimum value of the magnetic field to be applied parallel to the plates so that the current through the ammeter becomes zero is $\mathrm{B}\times {10}^{-5} \mathrm{T}$. Then the value of

$B$ is (mass of electron $=9.0\times {10}^{-31} \mathrm{kg}$, charge of electron $=1.6\times {10}^{-19}\mathrm{C}$ )

A proton (mass $m$) accelerated by a potential difference $V$ flies through a uniform transverse magnetic field $B$. The field occupies a region of space by width $d$. If $\alpha$ be the angle of deviation of proton from the initial direction of motion (see figure), the value of $\sin \alpha$ will be:

A uniform magnetic field acts at a right angle to the direction of motion of a charged particle. As a result, the charged particle moves in a circular path of radius $2 \mathrm{cm}$. If both the charge and speed of the charged particles are made double, then the radius of the circular path will be

A rectangular region of dimensions $w\times I\left(w<<I\right)$ has a constant magnetic field into the plane of the paper as shown. On one side the region is bounded by a screen. On the other side positive ions of mass $m$ and charge $q$ are accelerated from rest and towards the screen by a parallel plate capacitor at constant potential difference $V<0$, and come out through a small hole in the upper plate. Which one of the following statements is correct regarding the charge on the ions that hit the screen?