A very long straight wire carries a current $I$. At the instant when a charge $ + Q$ at point $P$ has velocity $\overrightarrow V $, as shown, the force on the charge is

A particle of mass $m$ and charge $q$ is in an electric and magnetic field given by

$\vec E = 2\hat i + 3\hat j ;\, B = 4\hat j + 6\hat k$

The charged particle is shifted from the origin to the point $P(x = 1 ;\, y = 1)$ along a straight path. The magnitude of the total work done is

Bob of a simple pendulum of length $l$ is made of iron . The pendulum is oscillating over a horizontal coil carrying direct current. If the time period of the pendulum is $T$ then

Two charged particles of mass $m$ and charge $q$ each are projected from origin simultaneously with same speed $V$ in transverse magnetic field. If ${\vec r_1}$ and ${\vec r_2}$ are the position vectors of particles (with respect to origin) at $t = \frac{{\pi m}}{{qB}}$ then the value of  ${\vec r_1}.{\vec r_2}$ at that time is

In case Hall effect for a strip having charge $Q$ and area of cross-section $A$, the Lorentz force is

If the direction of the initial velocity of the charged particle is perpendicular to the magnetic field, then the orbit will be   or  The path executed by a charged particle whose motion is perpendicular to magnetic field is