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)
Column 1 Wire A 
Column 2 Wire B 
Column 3 Wire C 

I  I = 2A Direction = $+\hat{j}$ X = 2 
(i)  I = 3A Direction = $\hat{j}$ X = 5 
(P)  I = 1A Direction = $+\hat{j}$ X = 1 
II  I = 3A Direction = $\hat{j}$ X = 5 
(ii) 
I = 4A
Direction = $\hat{j}$ X = 4

(Q) 
I = 5A
Direction = $+\hat{j}$ X = 3

III 
I = 1A
X = 1Direction = $+\hat{j}$ 
(iii) 
I = 2A
X = 2Direction = $+\hat{j}$ 
(R) 
I = 6A
X = 4Direction = $+\hat{j}$ 
IV  I = 4A Direction = $\hat{j}$ X = 4 
(iv) 
I = 1A
X = 1Direction = $+\hat{j}$ 
(S) 
I = 2A
X = 4Direction = $+\hat{j}$ 
In which case the magnitude of magnetic field at X = 2 will be $B=\frac{{\mu}_{0}}{\pi}?$
Column 1 Wire A 
Column 2 Wire B 
Column 3 Wire C 

I  I = 2A Direction = $+\hat{j}$ X = 2 
(i)  I = 3A Direction = $\hat{j}$ X = 5 
(P)  I = 1A Direction = $+\hat{j}$ X = 1 
II  I = 3A Direction = $\hat{j}$ X = 5 
(ii) 
I = 4A
Direction = $\hat{j}$ X = 4

(Q) 
I = 5A
Direction = $+\hat{j}$ X = 3

III 
I = 1A
X = 1Direction = $+\hat{j}$ 
(iii) 
I = 2A
X = 2Direction = $+\hat{j}$ 
(R) 
I = 6A
X = 4Direction = $+\hat{j}$ 
IV  I = 4A Direction = $\hat{j}$ X = 4 
(iv) 
I = 1A
X = 1Direction = $+\hat{j}$ 
(S) 
I = 2A
X = 4Direction = $+\hat{j}$ 
In which case the magnitude of magnetic field at X = 4 be $\frac{13}{6}\frac{{\mu}_{0}}{\pi}?$
Column 1 Wire A 
Column 2 Wire B 
Column 3 Wire C 

I  I = 2A Direction = $+\hat{j}$ X = 2 
(i)  I = 3A Direction = $\hat{j}$ X = 5 
(P)  I = 1A Direction = $+\hat{j}$ X = 1 
II  I = 3A Direction = $\hat{j}$ X = 5 
(ii) 
I = 4A
Direction = $\hat{j}$ X = 4

(Q) 
I = 5A
Direction = $+\hat{j}$ X = 3

III 
I = 1A
X = 1Direction = $+\hat{j}$ 
(iii) 
I = 2A
X = 2Direction = $+\hat{j}$ 
(R) 
I = 6A
X = 4Direction = $+\hat{j}$ 
IV  I = 4A Direction = $\hat{j}$ X = 4 
(iv) 
I = 1A
X = 1Direction = $+\hat{j}$ 
(S) 
I = 2A
X = 4Direction = $+\hat{j}$ 
In which case the magnitude of magnetic field at x = 3 be $\frac{2{\mu}_{0}}{\pi}?$
Use the following information to answer the next question
A coil of 50 turns and 20 mm radius is placed normally in a magnetic field, as shown in the given figure. After some time, the magnitude of the magnetic field changes from 0.31 T to 0.11 T and its direction reverses. An emf of 10 V is induced in the coil because of this change. 
In how much time does the strength of the magnetic field change in magnitude from 0.31 T to 0.11 T?
A square loop made up with conducting wire has uniform cross section area and uniform linear mass density as shown in fig. The length of one side of square loop is l meter.
Match the columnI with corresponding results of columnII. $\overrightarrow{\mathrm{B}}$ in columnI is a positive nonzero constant
ColumnI  ColumnII  
A  $\overrightarrow{\mathrm{B}}=\left({\mathrm{B}}_{\circ}\hat{\mathit{i}}\right)\mathrm{T}$  P  Magnitude of net force on loop is zero 
B  $\overrightarrow{\mathrm{B}}=\left({\mathrm{B}}_{\circ}\hat{j}\right)\mathrm{T}$  Q  Magnitude of net force on loop is $\sqrt{2}\mathrm{I}l{\mathrm{B}}_{\circ}$ 
C  $\overrightarrow{\mathrm{B}}={\mathrm{B}}_{\circ}\left(\hat{\mathrm{k}}\right)\mathrm{T}$  R  Magnitude of net torque on loop about centre is zero 
D  $\overrightarrow{\mathrm{B}}={\mathrm{B}}_{\circ}\left(\hat{i}+\hat{j}\right)\mathrm{T}$  S  Magnitude of net force on loop is ${\mathrm{B}}_{\circ}\mathrm{I}l$ newton 