Tag: magnetic field produced in a circular loop

Chose the correct statement from the following:

Two long parallel wires A and B separated by a distance d, carry currents $i _1$ and $i _2$ respectively in the same direction. Write the following steps in a sequential order to find the magnitude of the resultant magnetic field at a point 'P', which is between the wires and is a distance '$x$' from the wire A.
(All the physical quantities are measured in SI units)
(a) Note the given values of $i _1, i _2$, $d$ and $x$.
(b) Write the formula to find the magnetic field due to a long straight current carrying wire i.e. $\displaystyle B=\frac{\mu _0 i}{2 \pi r}$
(c) Find the directions of the magnetic field at 'P' due to two wires A and B, using right hand thumb rule.
(d) Determine the magnetic field at P due to wire A, using $B _1 \displaystyle = \frac{\mu _0 i _1}{2 \pi x}$
(e) If the directions of magnetic field are same, then the resultant magnitude is equal to the sum of $B _1$ and $B _2$.
(f) Determine the magnetic field $B _2$ due to wire B at point P, ie. $B _2 = \displaystyle \frac{\mu _o i _2}{2 \pi (d-x)}$
(g) If the directions of magnetic fields are opposite to each other, then the resultant magnitude is equal to the difference of $B _1$ and $B _2$.

Consider a region where both uniform electric and magnetic fields E and B are present both along the z-axis. A positively charged particle of charge and mass is released from the origin with an initial velocity ${{\text{V}} _e}\hat i$. Which of the following option(s) are correct?