NEW
New Website Launch
Experience the best way to solve previous year questions with mock tests (very detailed analysis), bookmark your favourite questions, practice etc...
1

### JEE Main 2019 (Online) 12th January Morning Slot

As shown in the figure, two infinitely long, identical wires are bent by 90o and placed in such a way that the segments LP and QM are along the x-axis, while segments PS and QN are parallel to the y-axis. If OP = OQ = 4cm, and the magnitude of the magnetic field at O is 10–4 T, and the two wires carry equal currents (see figure), the magnitude of the current in each wire and the direction of the magnetic field at O will be ($$\mu$$0 = 4$$\pi$$ $$\times$$ 10–7 NA–2) :

A
40 A, perpendicular into the page
B
40 A, perpendicular out of the page
C
20 A, perpendicular into the page
D
40 A, perpendicular out of the page

## Explanation

Magnetic field at 'O' will be done to 'PS' and 'QN' Only

i.e. B0 = BPS + BQN $$\to$$ Both inwards

Let current in each wire = i

$$\therefore$$  B0 = $${{{\mu _0}i} \over {4\pi d}} + {{{\mu _0}i} \over {4\pi d}}$$

or      10$$-$$4 = $${{{\mu _0}i} \over {2\pi d}}$$ = $${{2 \times {{10}^{ - 7}} \times i} \over {4 \times {{10}^{ - 2}}}}$$

$$\therefore$$       i = 20 A
2

### JEE Main 2019 (Online) 11th January Evening Slot

A particle of mass m and charge q is in an electric and magnetic field given by
$$\overrightarrow E = 2\widehat i + 3\widehat j;\,\,\,\overrightarrow B = 4\widehat j + 6\widehat k.$$

The charged particle is shifted from he origin to the point P(x = 1; y = 1) along a straight path. The magnitude of the total work done is :
A
(2.5) q
B
(0.35) q
C
(0.15) q
D
5 q

## Explanation

$${\overrightarrow F _{net}} = q\overrightarrow E + q\left( {\overrightarrow v \times \overrightarrow B } \right)$$

$$= \left( {2q\widehat i + 3q\widehat j} \right) + q\left( {\overrightarrow v \times \overrightarrow B } \right)$$

$$W = {\overrightarrow F _{net}}.\overrightarrow S$$

$$=$$ 2q + 3q

$$=$$ 5q
3

### JEE Main 2019 (Online) 11th January Evening Slot

The region between y = 0 and y = d contains a magnetic field $$\overrightarrow B = B\widehat z$$. A particle of mass m and charge q enters the region with a velocity $$\overrightarrow v = v\widehat i.$$ If d $$=$$ $${{mv} \over {2qB}},$$ the acceleration of the charged particle at the point of its emergence at the other side is :
A
$${{qvB} \over m}\left( -{{{\sqrt 3 } \over 2}\widehat i - {1 \over 2}\widehat j} \right)$$
B
$${{qvB} \over m}\left( {{1 \over 2}\widehat i - {{\sqrt 3 } \over 2}\widehat j} \right)$$
C
$${{qvB} \over m}\left( {{{ - \widehat j + \widehat i} \over {\sqrt 2 }}} \right)$$
D
$${{qvB} \over m}\left( {{{\widehat j + \widehat i} \over {\sqrt 2 }}} \right)$$

## Explanation

Here R = $${{mv} \over {qB}}$$ = 2d

cos $$\theta$$ = $${{{R \over 2}} \over R}$$ = $${1 \over 2}$$

$$\Rightarrow$$ $$\theta$$ = 60o

Acceleration of the charged particle at the point of its emergence,

$$\overrightarrow {{a_c}} = {a_{{c_x}}}\left( { - \widehat i} \right) + {a_{{c_y}}}\left( { - \widehat j} \right)$$

= $${a_c}\cos 30^\circ \left( { - \widehat i} \right) + {a_c}\sin 30^\circ \left( { - \widehat j} \right)$$

= $${a_c}\left( {{{\sqrt 3 } \over 2}\left( { - \widehat i} \right) + {1 \over 2}\left( { - \widehat j} \right)} \right)$$

= $${{qvB} \over m}\left( { - {{\sqrt 3 } \over 2}\widehat i - {1 \over 2}\widehat j} \right)$$
4

### JEE Main 2019 (Online) 11th January Morning Slot

There are two long co-axial solenoids of same length $$l$$. The inner and outer coils have radii r1 and r2 and number of turns per unit length n1 and n2, respectively. The ratio of mutual inductance to the self - inductance of the inner-coil is :
A
$${{{n_2}} \over {{n_1}}}.{{{r_2}^2} \over {{r_1}^2}}$$
B
$${{{n_2}} \over {{n_1}}}$$
C
$${{{n_1}} \over {{n_2}}}$$
D
$${{{n_2}} \over {{n_1}}}.{{{r_1}} \over {{r_2}}}$$

## Explanation

$$M = {\mu _0}\,{n_1}\,{n_2}\,\pi r_1^2$$

$$L = {\mu _0}\,n_1^2\,\pi r_1^2$$

$$\Rightarrow \,\,{M \over L} = {{{n_2}} \over {{n_1}}}$$

### Joint Entrance Examination

JEE Main JEE Advanced WB JEE

### Graduate Aptitude Test in Engineering

GATE CSE GATE ECE GATE EE GATE ME GATE CE GATE PI GATE IN

NEET

Class 12