$A$ uniform beam of positively charged particles is moving with a constant velocity parallel to another beam of negatively charged particles moving with the same velocity in the opposite direction,separated by a distance $d$. The variation of the magnetic field $B$ along a perpendicular line drawn between the two beams is best represented by:

Two wires each carrying a steady current $I$ are shown in four configurations in Column $I$. Some of the resulting effects are described in Column $II$. Match the statements in Column $I$ with the statements in Column $II$.

Column $I$	Column $II$
$(A)$ Two parallel wires with current in the same direction,$P$ is the midpoint.	$(p)$ The magnetic fields $(B)$ at $P$ due to the currents in the wires are in the same direction.
$(B)$ Two coaxial circular loops with current in the same direction,$P$ is the midpoint on the axis.	$(q)$ The magnetic fields $(B)$ at $P$ due to the currents in the wires are in opposite directions.
$(C)$ Two coplanar circular loops with current in opposite directions,$P$ is the midpoint.	$(r)$ There is no magnetic field at $P$.
$(D)$ Two concentric coplanar circular loops with current in the same direction,$P$ is the common center.	$(s)$ The wires repel each other.

$A$ loop of irregular shape made of flexible conducting wire carrying a clockwise current is placed in a uniform inward magnetic field,such that its plane is perpendicular to the field. Then the loop:

$A$ charged particle (electron or proton) is introduced at the origin $(x=0, y=0, z=0)$ with a given initial velocity $\overrightarrow{v}$. $A$ uniform electric field $\overrightarrow{E}$ and magnetic field $\vec{B}$ are given in columns $I, II$ and $III$, respectively. The quantities $E_0, B_0$ are positive in magnitude.

Column $I$	Column $II$	Column $III$
$(I)$ Electron with $\overrightarrow{v}=2 \frac{E_0}{B_0} \hat{x}$	$(i)$ $\overrightarrow{E}=E_0 \hat{z}$	$(P)$ $\overrightarrow{B}=-B_0 \hat{x}$
$(II)$ Electron with $\overrightarrow{v}=\frac{E_0}{B_0} \hat{y}$	$(ii)$ $\overrightarrow{E}=-E_0 \hat{y}$	$(Q)$ $\overrightarrow{B}=B_0 \hat{x}$
$(III)$ Proton with $\overrightarrow{v}=0$	$(iii)$ $\overrightarrow{E}=-E_0 \hat{x}$	$(R)$ $\overrightarrow{B}=B_0 \hat{y}$
$(IV)$ Proton with $\overrightarrow{v}=2 \frac{E_0}{B_0} \hat{x}$	$(iv)$ $\overrightarrow{E}=E_0 \hat{x}$	$(S)$ $\overrightarrow{B}=B_0 \hat{z}$

$(1)$ In which case will the particle move in a straight line with constant velocity?
$(2)$ In which case will the particle describe a helical path with axis along the positive $z$ direction?
$(3)$ In which case would the particle move in a straight line along the negative direction of $y$-axis (i.e., move along $-\hat{y}$)?

Two long straight parallel wires are a distance $2d$ apart. They carry steady equal currents flowing out of the plane of the paper. The variation of magnetic field $B$ along the line $xx'$ is given by:

Choose the correct sketch of the magnetic field lines for a pair of parallel current-carrying wires,one with current flowing into the plane (represented by $\otimes$) and one with current flowing out of the plane (represented by $\odot$).