Moving Charges and Magnetism
A charged particle (electron or proton) is introduced at the origin (x = 0, y = 0, z = 0) with a given initial velocity $\overrightarrow{\mathrm{v}}$. A uniform electric field $\overrightarrow{\mathrm{E}}$ and a uniform magnetic field $\overrightarrow{\mathrm{B}}$ exist everywhere. The velocity $\overrightarrow{\mathrm{v}}$ , electric field $\overrightarrow{\mathrm{E}}$ and magnetic field $\overrightarrow{\mathrm{B}}$ are given in column 1, 2 and 3, respectively. The quantities E_{0}, B_{0} are positive in magnitude. 

Column1  Column2  Column3 
(I) Electron with $\overrightarrow{\mathrm{v}}=2\frac{{\mathrm{E}}_{0}}{{\mathrm{B}}_{0}}\hat{\mathrm{x}}$  (i) $\overrightarrow{\mathrm{E}}={\mathrm{E}}_{0}\hat{\mathrm{z}}$  (P) $\overrightarrow{\mathrm{B}}={\mathrm{B}}_{0}\hat{\mathrm{x}}$ 
(II) Electron with $\overrightarrow{\mathrm{v}}=\frac{{\mathrm{E}}_{0}}{{\mathrm{B}}_{0}}\hat{\mathrm{y}}$  (ii) $\overrightarrow{\mathrm{E}}={\mathrm{E}}_{0}\hat{\mathrm{y}}$  (Q) $\overrightarrow{\mathrm{B}}={\mathrm{B}}_{0}\hat{\mathrm{x}}$ 
(III) Proton with $\overrightarrow{\mathrm{v}}=0$  (iii) $\overrightarrow{\mathrm{E}}={\mathrm{E}}_{0}\hat{\mathrm{x}}$  (R) $\overrightarrow{\mathrm{B}}={\mathrm{B}}_{0}\hat{\mathrm{y}}$ 
(IV) Proton with $\overrightarrow{\mathrm{v}}=2\frac{{\mathrm{E}}_{0}}{{\mathrm{B}}_{0}}\hat{\mathrm{x}}$  (iv) $\overrightarrow{\mathrm{E}}={\mathrm{E}}_{0}\hat{\mathrm{x}}$  (S) $\overrightarrow{\mathrm{B}}={\mathrm{B}}_{0}\hat{\mathrm{z}}$ 
In which case would the particle move in a straight line along the negative direction of yaxis (i.e., move along $\hat{\mathrm{y}}$) ?
PARAGRAPH 2
In a thin rectangular metallic strip a constant current I flows along the positive x–direction, as shown in the figure. The length, width and thickness of the strip are ℓ, w and d, respectively.A uniform magnetic field $\overrightarrow{\mathrm{B}}$ is applied on the strip along the positive y–direction. Due to this, the charge carriers experience a net deflection along the z–direction. This results in accumulation of charge carriers on the surface PQRS and appearance of equal and opposite charges on the face opposite to PQRS. A potential difference along the z–direction is thus developed. Charge accumulation continues until the magnetic force is balanced by the electric force. The current is assumed to be uniformly distributed on the cross section of the strip and carried by electrons. 
Consider two different metallic strips (1 and 2) of same dimensions (length ℓ, width w and thickness d) with carrier densities n_{1} and n_{2} respectively. Strip 1 is placed in magnetic field B_{1} and strip 2 is placed in magnetic field B_{2}, both along positive y–directions. Then V_{1} and V_{2} are the potential differences developed between K and M in strips 1 and 2, respectively. Assuming that the current I is the same for both the strips, the correct option(s) is (are)
Six point charges, each of the same magnitude q, are arranged in different manners as shown in Column II. In each case, a point M and a line PQ passing through M are shown. Let E be the electric field and V be the electric potential at M(Potential at infinity is zero) due to the given charge distribution when it is at rest. Now, the whole system is set into rotation with a constant angular velocity about the line PQ. Let B the magnetic field at M and be the magnetic moment of the system in this condition. Assume each rotating charge to be equivalent to a steady current.
Column I 
Column II 

(A) 
E = 0 
(p) 
Charges are at the corners of a regular hexagon. M is at the centre of the hexagone. PQ is perpendicular to the plane of the hexagone 
(B) 
(q) 
Charges are on a line perpendicular to PQ at equal intervals. M is the midpoint between the two innermost charges 

(C) 
B = 0 
(r) 
Charges are placed on two coplanar insulating rings at equal intervals. M is the common centre of the rings. PQ is perpendicular to the plane of the rings 
(D) 
(s) 
Charges are placed at the corners of a rectangle of sides a and 2a and at the mid points of the longer sides. M is at the centre of the rectangle. Pq is parallel to the longer sides. 

(t) 
Charges are placed on two coplanar, identical insulating rings at equal intervals. M is the mid points between the centres of the line joining the centres and coplanar to the rings. 
Column I  Column II 
(A) Dielectric ring uniformly charged  (P) Time independent electrostatic field out of system 
(B) Dielectric ring uniformly charged rotating with angular velocity $\omega $  (Q) Magnetic field 
(C) Constant current in ring ${i}_{o}$  (R) Induced electric field 
(D) $i={i}_{0}\mathrm{cos}\omega t$  (S) Magnetic moment 