A particle of mass M and positive charge Q , moving with a constant velocity u → 1 = 4 i ^ m s - 1 , enters a region of uniform static magnetic field normal to the x - y plane. The region of the magnetic field extends from x = 0 to x = L for all values of y . After passing through this region, the particle emerges on the other side after 10 milliseconds with a velocity u → 2 = 2 3 i ^ + j ^ m s - 1 . The correct statement (s) is (are)

The magnitude of the magnetic field 5 0 π M 3 Q units.

The direction of the magnetic field is +z direction.

The magnitude of the magnetic field 1 0 0 π M 3 Q units.

In a certain region static electric and magnetic fields exist. The magnetic field is given by B → = B 0 i ^ + 2 j ^ - 4 k ^ . If a test charge moving with a velocity v → = v 0 3 i ^ - j ^ + 2 k ^ experiences no force in that region, then the electric field in the region, in SI units, is:

E → = - v 0 B 0 14 j ^ + 7 k ^

E → = - v 0 B 0 i ^ + j ^ + 7 k ^

E → = - υ 0 B 0 3 i ^ - 2 j ^ - 4 k ^

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In a region, magnetic field along $x -$ axis changes according to the graph given in figure.

If time period, pitch and radius of helix path are $T_{0}, P_{0},$ and $R_{0},$ respectively, and if the particle is projected at an angle $θ_{0}$ with the positive $x -$ axis toward positive y-axis in $x - y$ plane, then
Select the correct statement:

Important Questions on Magnetic Effect of Current

HARD

Physics>Electricity and Magnetism>Magnetic Effect of Current>Lorentz Force

In the

xy - plane

, the region

y > 0

has a uniform magnetic field

B_{1} \hat{k}

and the region

y < 0

has another uniform magnetic field

B_{2} \hat{k}

. A positively charged particle is projected from the origin along the positive

y - axis

with speed

v_{0} = π m s^{- 1}

t = 0

, as shown in the figure. Neglect gravity in this problem. Let

t = T

be the time when the particle crosses the

x - axis

from below for the first time. If

B_{2} = 4 B_{1}

, the average speed of the particle, in

m s^{- 1}

, along the

x - axis

in the time interval

T

is ________.

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EASY

Physics>Electricity and Magnetism>Magnetic Effect of Current>Lorentz Force

A proton with a kinetic energy of

2.0 eV

moves into a region of uniform magnetic field of magnitude

\frac{π}{2} \times 10^{- 3} T

. The angle between the direction of magnetic field and velocity of proton is

60^{o}

. The pitch of the helical path taken by the proton is ____

cm

. (Take, mass of proton

= 1.6 \times 10^{- 27} kg

and charge on proton

= 1.6 \times 10^{- 19} C

MEDIUM

Physics>Electricity and Magnetism>Magnetic Effect of Current>Lorentz Force

A proton and an

α

- particle (with their masses in the ratio of

1 : 4

and charges in the ratio of

1 : 2

) are accelerated from rest through a potential difference

V .

If a uniform magnetic field

(B)

is set up perpendicular to their velocities, the ratio of the radii

r_{p} : r_{α}

of the circular paths described by them will be:

HARD

Physics>Electricity and Magnetism>Magnetic Effect of Current>Lorentz Force

If one were to apply the Bohr model to a particle of mass

' m'

and charge

' q'

moving in a plane under the influence of a magnetic field 'B', the energy of the charged particle in the

n^{t h}

level will be:

MEDIUM

Physics>Electricity and Magnetism>Magnetic Effect of Current>Lorentz Force

A beam of protons with velocity

600 km s^{- 1}

enters a uniform magnetic field of

0.2 T

. The velocity makes an angle of

30 °

with the magnetic field. The radius of the helical path will be

MEDIUM

Physics>Electricity and Magnetism>Magnetic Effect of Current>Lorentz Force

A proton (mass $m$ ) accelerated by a potential difference $V$ flies through a uniform transverse magnetic field $B$ . The field occupies a region of space by width $d$ . If $α$ be the angle of deviation of proton from the initial direction of motion (see figure), the value of $\sin α$ will be:
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EASY

Physics>Electricity and Magnetism>Magnetic Effect of Current>Lorentz Force

A charge particle moving in magnetic field

B,

has the components of velocity along

B

as well as perpendicular to

B

. The path of the charge particle will be

EASY

Physics>Electricity and Magnetism>Magnetic Effect of Current>Lorentz Force

A negative test charge is moving near a long straight wire carrying a current. The force acting on the test charge is parallel to the direction of the current. The motion of the charge is:

MEDIUM

Physics>Electricity and Magnetism>Magnetic Effect of Current>Lorentz Force

A particle of mass

m

and charge

q

with an initial velocity

v

is subjected to a uniform magnetic field

B

along the vertical direction. The particle will

MEDIUM

Physics>Electricity and Magnetism>Magnetic Effect of Current>Lorentz Force

When a charged particle enters a magnetic field at an angle of

60 °

with the field direction, it traces

MEDIUM

Physics>Electricity and Magnetism>Magnetic Effect of Current>Lorentz Force

An electron is moving in a circular path under the influence of a transverse magnetic field of

3.57 \times 10^{- 2} T

. If, the value of

\frac{e}{m}

1 .76 \times 10^{11} C {kg}^{- 1}

, the frequency of revolution of the electron is

MEDIUM

Physics>Electricity and Magnetism>Magnetic Effect of Current>Lorentz Force

A beam of protons with speed

4 \times 10^{5} m s^{- 1}

enters a uniform magnetic field of

0.3 T

at an angle

60 °

to the magnetic field, the pitch of the resulting helical path of protons is close to : (Mass of the proton

= 1.67 \times 10^{- 27} kg

, charge of the proton

= 1.69 \times 10^{- 19} C

)

HARD

Physics>Electricity and Magnetism>Magnetic Effect of Current>Lorentz Force

A particle of mass

M

and positive charge

Q

, moving with a constant velocity

{\vec{u}}_{1} = 4 \hat{i} m s^{- 1}

, enters a region of uniform static magnetic field normal to the

x - y

plane. The region of the magnetic field extends from

x = 0

x = L

for all values of

y

. After passing through this region, the particle emerges on the other side after 10 milliseconds with a velocity

{\vec{u}}_{2} = 2 (\sqrt{3} \hat{i} + \hat{j}) m s^{- 1}

. The correct statement (s) is (are)

EASY

Physics>Electricity and Magnetism>Magnetic Effect of Current>Lorentz Force

A proton and an alpha particle both enter a region of uniform magnetic field B, moving at right angles to the field B. if the radius of circular orbits for both the particles is equal and the kinetic energy acquired by proton is 1 MeV, the energy acquired by the alpha particle will be:

MEDIUM

Physics>Electricity and Magnetism>Magnetic Effect of Current>Lorentz Force

In a certain region static electric and magnetic fields exist. The magnetic field is given by

\vec{B} = B_{0} (\hat{i} + 2 \hat{j} - 4 \hat{k})

. If a test charge moving with a velocity

\vec{v} = v_{0} (3 \hat{i} - \hat{j} + 2 \hat{k})

experiences no force in that region, then the electric field in the region, in SI units, is:

EASY

Physics>Electricity and Magnetism>Magnetic Effect of Current>Lorentz Force

A proton, a deuteron and an

α

-particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is :

MEDIUM

Physics>Electricity and Magnetism>Magnetic Effect of Current>Lorentz Force

An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii

r_{e}, r_{p}, r_{α}

respectively in a uniform magnetic field B. The relation between

r_{e}, r_{p}, r_{α}

is:

HARD

Physics>Electricity and Magnetism>Magnetic Effect of Current>Lorentz Force

An electron is moving in a uniform magnetic field

\vec{B}

. The velocity

\vec{v}

of the electron is directed at an angle

θ

to the direction of the field where

\tan θ = \frac{3}{4}

. If the speed of the electron is

4 \times 10^{6} m s^{- 1}

and the strength of the magnetic field is

0.18 T

, then the distance moved by the electron along the field direction in the time it takes for the electron to complete one full orbit is approximately

EASY

Physics>Electricity and Magnetism>Magnetic Effect of Current>Lorentz Force

A particle of mass

m

and charge

q

is incident on

X Z

plane with velocity

v

in a direction making angle

θ

with a uniform magnetic field applied along

X

-axis. The nature of motion performed by the particle is

MEDIUM

Physics>Electricity and Magnetism>Magnetic Effect of Current>Lorentz Force

The figure shows a region of length ' $l$ ' with a uniform magnetic field of $0.3 T$ in it and a proton entering the region with velocity $4 \times 10^{5} m s^{- 1}$ making an angle $60 °$ with the field. If the proton completes $10$ revolution by the time it cross the region shown, ' $l$ ' is close to (mass of proton $= 1.67 \times 10^{- 27} kg$ , charge of the proton $= 1.6 \times 10^{- 19} C$ )

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Important Questions on Magnetic Effect of Current

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