A symmetric star shaped conducting wire loop is carrying a steady state current $${\rm I}$$ as shown in the figure. The distance between the diametrically opposite vertices of the star is $$4a.$$ The magnitude of the magnetic field at the center of the loop is

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 a uniform magnetic field $$\overrightarrow B $$ exist everywhere. The velocity $$\overrightarrow v ,$$ electric field $$\overrightarrow E $$ and magnetic field $$\overrightarrow B $$ are given in column $$1,2$$ and $$3,$$ respectively. The quantities $${E_0},{B_0}$$ are positive in magnitude.

Column 1		Column 2		Column 3
(I)	Electron with $$\overrightarrow v = 2{{{E_0}} \over {{B_0}}}\widehat x$$	(i)	$$\overrightarrow E = {E_0}\widehat z$$	(P)	$$\overrightarrow B = - {B_0}\widehat x$$
(II)	Electron with $$\overrightarrow v = {{{E_0}} \over {{B_0}}}\widehat y$$	(ii)	$$\overrightarrow E = - {E_0}\widehat y$$	(Q)	$$\overrightarrow B = {B_0}\widehat x$$
(III)	Proton with $$\overrightarrow v = 0$$	(iii)	$$\overrightarrow E = - {E_0}\widehat x$$	(R)	$$\overrightarrow B = {B_0}\widehat y$$
(IV)	Proton with $$\overrightarrow v = 2{{{E_0}} \over {{B_0}}}\widehat x$$	(iv)	$$\overrightarrow E = {E_0}\widehat x$$	(S)	$$\overrightarrow B = {B_0}\widehat z$$

In which case will the particle move in a straight line with constant velocity?

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 a uniform magnetic field $$\overrightarrow B $$ exist everywhere. The velocity $$\overrightarrow v ,$$ electric field $$\overrightarrow E $$ and magnetic field $$\overrightarrow B $$ are given in column $$1,2$$ and $$3,$$ respectively. The quantities $${E_0},{B_0}$$ are positive in magnitude.

Column 1		Column 2		Column 3
(I)	Electron with $$\overrightarrow v = 2{{{E_0}} \over {{B_0}}}\widehat x$$	(i)	$$\overrightarrow E = {E_0}\widehat z$$	(P)	$$\overrightarrow B = - {B_0}\widehat x$$
(II)	Electron with $$\overrightarrow v = {{{E_0}} \over {{B_0}}}\widehat y$$	(ii)	$$\overrightarrow E = - {E_0}\widehat y$$	(Q)	$$\overrightarrow B = {B_0}\widehat x$$
(III)	Proton with $$\overrightarrow v = 0$$	(iii)	$$\overrightarrow E = - {E_0}\widehat x$$	(R)	$$\overrightarrow B = {B_0}\widehat y$$
(IV)	Proton with $$\overrightarrow v = 2{{{E_0}} \over {{B_0}}}\widehat x$$	(iv)	$$\overrightarrow E = {E_0}\widehat x$$	(S)	$$\overrightarrow B = {B_0}\widehat z$$

In which case will the particle describe a helical path with axis along the positive $$z$$ direction?

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 a uniform magnetic field $$\overrightarrow B $$ exist everywhere. The velocity $$\overrightarrow v ,$$ electric field $$\overrightarrow E $$ and magnetic field $$\overrightarrow B $$ are given in column $$1,2$$ and $$3,$$ respectively. The quantities $${E_0},{B_0}$$ are positive in magnitude.

Column 1		Column 2		Column 3
(I)	Electron with $$\overrightarrow v = 2{{{E_0}} \over {{B_0}}}\widehat x$$	(i)	$$\overrightarrow E = {E_0}\widehat z$$	(P)	$$\overrightarrow B = - {B_0}\widehat x$$
(II)	Electron with $$\overrightarrow v = {{{E_0}} \over {{B_0}}}\widehat y$$	(ii)	$$\overrightarrow E = - {E_0}\widehat y$$	(Q)	$$\overrightarrow B = {B_0}\widehat x$$
(III)	Proton with $$\overrightarrow v = 0$$	(iii)	$$\overrightarrow E = - {E_0}\widehat x$$	(R)	$$\overrightarrow B = {B_0}\widehat y$$
(IV)	Proton with $$\overrightarrow v = 2{{{E_0}} \over {{B_0}}}\widehat x$$	(iv)	$$\overrightarrow E = {E_0}\widehat x$$	(S)	$$\overrightarrow B = {B_0}\widehat z$$

In which case would the particle move in a straight line along the negative direction of $$y$$-axis (i.e., move along $$ - \widehat y$$)?