1
JEE Advanced 2017 Paper 2 Offline
+3
-0.75
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
$${{{\mu _0}1} \over {4\pi a}}6\left[ {\sqrt 3 - 1} \right]$$
B
$${{{\mu _0}1} \over {4\pi a}}6\left[ {\sqrt 3 + 1} \right]$$
C
$${{{\mu _0}1} \over {4\pi a}}3\left[ {\sqrt 3 - 1} \right]$$
D
$${{{\mu _0}1} \over {4\pi a}}3\left[ {2 - \sqrt 3 } \right]$$
2
JEE Advanced 2017 Paper 1 Offline
+3
-0.75
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
$$\left( {{\rm I}{\rm I}{\rm I}} \right)\left( {ii} \right)\left( R \right)$$
B
$$\left( {{\rm I}V} \right)\left( i \right)\left( S \right)$$
C
$$\left( {{\rm I}{\rm I}{\rm I}} \right)\left( {iii} \right)\left( P \right)$$
D
$$\left( {{\rm I}{\rm I}} \right)\left( {iii} \right)\left( S \right)$$
3
JEE Advanced 2017 Paper 1 Offline
+3
-0.75
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
$$\left( {{\rm I}V} \right)\left( i \right)\left( S \right)$$
B
$$\left( {{\rm I}{\rm I}} \right)\left( {ii} \right)\left( R \right)$$
C
$$\left( {{\rm I}{\rm I}{\rm I}} \right)\left( {iii} \right)\left( P \right)$$
D
$$\left( {{\rm I}V} \right)\left( {ii} \right)\left( R \right)$$
4
JEE Advanced 2017 Paper 1 Offline
+3
-0.75
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 $$- \widehat y$$)?
A
$$\left( {{\rm I}{\rm I}} \right)\left( {iii} \right)\left( Q \right)$$
B
$$\left( {{\rm I}{\rm I}{\rm I}} \right)\left( {ii} \right)\left( R \right)$$
C
$$\left( {{\rm I}V} \right)\left( {ii} \right)\left( S \right)$$
D
$$\left( {{\rm I}{\rm I}{\rm I}} \right)\left( {ii} \right)\left( P \right)$$
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