1
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
$$\left( {{\rm I}V} \right)\left( {ii} \right)\left( R \right)$$
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 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
$$\left( {{\rm I}{\rm I}{\rm I}} \right)\left( {ii} \right)\left( P \right)$$
3
JEE Advanced 2014 Paper 2 Offline
+3
-1

The figure shows a circular loop of radius a with two long parallel wires (numbered 1 and 2) all in the plane of the paper. The distance of each wire from the centre of the loop is d. The loop and the wires are carrying the same current I. The current in the loop is in the counter clockwise direction if seen from above. When d $$\approx$$ a but wires are not touching the loop, it is found that the net magnetic field on the axis of the loop is zero at a height h above the loop. In that case

A
current in wire 1 and wire 2 is the direction PQ and RS, respectively, and h $$\approx$$ a.
B
current in wire 1 and wire 2 is the direction PQ and SR, respectively, and h $$\approx$$ a.
C
current in wire 1 and wire 2 is the direction PQ and SR, respectively, and h $$\approx$$ 1.2a.
D
current in wire 1 and wire 2 is the direction PQ and RS, respectively, and h $$\approx$$ 1.2a.
4
JEE Advanced 2014 Paper 2 Offline
+3
-1

The figure shows a circular loop of radius a with two long parallel wires (numbered 1 and 2) all in the plane of the paper. The distance of each wire from the centre of the loop is d. The loop and the wires are carrying the same current I. The current in the loop is in the counter clockwise direction if seen from above. Consider d >> a, and the loop is rotated about its diameter parallel to the wires by 30$$^\circ$$ from the position shown in the below figure. If the currents in the wires are in the opposite directions, the torque on the loop at its new position will be (assume that the net field due to the wires is constant over the loop)

A
$${{{\mu _0}{I^2}{a^2}} \over d}$$
B
$${{{\mu _0}{I^2}{a^2}} \over {2d}}$$
C
$${{\sqrt 3 {\mu _0}{I^2}{a^2}} \over d}$$
D
$${{\sqrt 3 {\mu _0}{I^2}{a^2}} \over {2d}}$$
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