The electric fields of two plane electromagnetic plane waves in vacuum are given by E 1 → = E 0 cos ω t - k x j ^ and E 2 → = E 0 cos ω t - k y k ^ , at t = 0 , a particle of charge q is at origin with a velocity v → = 08 c j ^ ( c is the speed of light in vaccum). The instantaneous force experienced by the particle is:

E 0 q 0 .8 i ^ + j ^ + 0 .2 k ^

E 0 q 0 .8 i ^ - j ^ + 0 .4 k ^

E 0 q 0 .4 i ^ - 3 j ^ + 0 .8 k ^

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 ^

A charged particle carrying charge 1 μ C is moving with velocity ( 2 i ^ + 3 j ^ + 4 k ^ ) m s - 1 . If an external magnetic field of ( 5 i ^ + 3 j ^ - 6 k ^ ) × 10 - 3 T exists in the region where the particle is moving then the force on the particle is F → × 10 - 9 N . the vector F → is :

- 0 . 30 i ^ + 0 . 32 j ^ - 0 . 09 k ^

- 3 . 0 i ^ + 32 j ^ - 0 . 9 k ^

An electron enters a magnetic field of 3 i ^ + 4 j ^ T with a velocity of 6 j ^ + 4 k ^ m s - 1 . The acceleration produced is ( e m of electron = 1 . 76 × 10 11 C kg - 1 )

3 . 52 - 8 i ^ + 6 j ^ - 9 k ^ × 10 11 m s - 2

2 . 53 - 8 i ^ - 6 j ^ + 9 k ^ × 10 11 m s - 2

1 . 76 - 8 i ^ - 6 j ^ + 9 k ^ × 10 11 m s - 2

3 . 52 - 8 i ^ + 6 j ^ - 9 k ^ m s - 2

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C.G.S. unit of magnetic field intensity is Gauss.

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Important Questions on Magnetic Fields due to Electric Current

MEDIUM

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Magnetic Force

The magnitude of the magnetic field at the centre of an equilateral triangular loop of side

1 m

which is carrying a current of

10 A

is:
[Take

μ_{0} = 4 π \times 10^{- 7} N A^{- 2}

]

MEDIUM

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Magnetic Force

A wire bent in the shape of a regular

n

polygonal loop carries a steady current

I

. Let

l

be the perpendicular distance of a given segment and

R

be the distance of a vertex both from the centre of the loop. The magnitude of the magnetic field at the centre of the loop is given by,

MEDIUM

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Magnetic Force

Two magnetic dipoles $X$ and $Y$ are placed at a separation $d$ , with their axes perpendicular to each other. The dipole moment of $Y$ is twice that of $X$ . A particle of charge $q$ is passing through their mid-point $P$ , at angle $θ = 45^{o}$ with the horizontal line, as shown in figure. What would be the magnitude of force on the particle at that instant? ( $d$ is much larger than the dimension of the dipole)
Question Image

EASY

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Magnetic Force

The magnetic induction field has the dimensions of

MEDIUM

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Magnetic Force

An electron enters a chamber in which a uniform magnetic field is present as shown.
Question Image

An electric field of appropriate magnitude is also applied so that the electron travels un-deviated without any change in its speed through the chamber. We are ignoring gravity. Then, the direction of the electric field is,

MEDIUM

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Magnetic Force

The electric fields of two plane electromagnetic plane waves in vacuum are given by

\vec{E_{1}} = E_{0} \cos (ω t - k x) \hat{j}

and

\vec{E_{2}} = E_{0} \cos (ω t - k y) \hat{k}

, at

t = 0,

a particle of charge

q

is at origin with a velocity

\vec{v} = 08 c \hat{j}

(

c

is the speed of light in vaccum). The instantaneous force experienced by the particle is:

EASY

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Magnetic 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 :

EASY

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Magnetic Force

A charged particle moves through a magnetic field perpendicular to its direction. Then

MEDIUM

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Magnetic Force

A particle of charge

Q

moves with a velocity

v = a \hat{i}

in a magnetic field

B = b \hat{j} + c \hat{k}

where

a, b

and

c

are constants. The magnitude of the force experienced by the particle is

MEDIUM

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Magnetic 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 Fields due to Electric Current>Magnetic Force

A charged particle carrying charge

1 μ C

is moving with velocity

(2 \hat{i} + 3 \hat{j} + 4 \hat{k}) m s^{- 1}

. If an external magnetic field of

(5 \hat{i} + 3 \hat{j} - 6 \hat{k}) \times 10^{- 3} T

exists in the region where the particle is moving then the force on the particle is

\vec{F} \times 10^{- 9} N

. the vector

\vec{F}

is :

EASY

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Magnetic Force

What is the importance of Oersted's experiment?

MEDIUM

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Magnetic Force

A particle of charge

q

and mass

m

is moving with a velocity

- v \hat{i} (v \neq 0)

towards a large screen placed in the

Y - Z

plane at distance d. If there is magnetic field

\vec{B} = B_{0} \hat{k},

the minimum value of

v

for which the particle will not hit the screen is :

EASY

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Magnetic Force

A circular coil of wire consisting of

100

turns each of radius

9 cm

carries a current of

0.4 A

. The magnitude of the magnetic field at the centre of coil is

(μ_{0} = 12.56 \times 10^{- 7} SI Units)

EASY

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Magnetic Force

The work done by a uniform magnetic field on a moving charge is,

HARD

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Magnetic Force

An electron enters a magnetic field of $(3 \hat{i} + 4 \hat{j}) T$ with a velocity of $(6 \hat{j} + 4 \hat{k}) m s^{- 1} .$ The acceleration produced is

( $\frac{e}{m}$ of electron $= 1.76 \times 10^{11} C {kg}^{- 1}$ )

EASY

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Magnetic Force

A charge

q_{o}

moving with velocity

\vec{v}

in a magnetic field of induction

\vec{B}

, experiences force

\vec{F}

. The angle between

\vec{v}

and

\vec{B}

θ .

The speed of

q_{o}

after one second will be

MEDIUM

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Magnetic Force

An electron enters a chamber in which a uniform magnetic field is present as shown. Ignore gravity
Question Image

During its motion inside the chamber

HARD

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Magnetic 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:

EASY

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Magnetic Force

A magnetic field cannot

C.G.S. unit of magnetic field intensity is Gauss.

Important Questions on Magnetic Fields due to Electric Current

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