Tag: magnetic effects of current and magnetism

Questions Related to magnetic effects of current and magnetism

If E and B denote electronic and magnetic field respectively, which of the following is dimensionless?

properties of magnet magnetic field moving charges and magnetism magnetic effects of current and magnetism physics

  1. $\sqrt { { \mu } _{ 0 }{ \varepsilon } _{ 0 } } \dfrac { E }{ B } $

  2. $ { { \mu } _{ 0 }{ \varepsilon } _{ 0 } } \dfrac { E }{ B } $

  3. ${ \mu } _{ 0 }{ \varepsilon } _{ 0 }{ \left( \dfrac { B }{ E } \right) }^{ 2 }$

  4. $\dfrac { E }{ { \varepsilon } _{ 0 } } \dfrac { { \mu } _{ 0 } }{ B } $

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Correct Option: A
Explanation:

We know that Velocity of light  $C _0=\dfrac{1}{\sqrt{\mu _0 \epsilon _0}}$

And also velocity of electromagnetic wave $V=\dfrac{E}{B}$
 $[C _0]=\left[\dfrac{1}{\sqrt{\mu _0 \epsilon _0}}\right]=[LT^{-1}]$

 $[V]=\left[\dfrac{E}{B}\right]=[LT^{-1}]$

$\left[\sqrt { { \mu } _{ 0 }{ \varepsilon } _{ 0 } } \dfrac { E }{ B } \right]=[LT^{-1}]^{-1}[LT^{-1}]=[M^0L^0T^0]$    (Dimention less),

Option A

Ratio of magnetic fields at 10 cm and 20 cm from a infinitely long current carrying wire is

properties of magnet magnetic field moving charges and magnetism magnetic effects of current and magnetism physics

  1. 1 : 2

  2. 1 : 4

  3. 2 : 1

  4. 4 : 1

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Correct Option: A

A large metal sheet carries an electric current along its surface. Current per unit length is $\lambda $. Magnetic field near the metal sheet is

properties of magnet magnetic field moving charges and magnetism magnetic effects of current and magnetism physics

  1. $\dfrac{\lambda { \mu } _{ 0 }}{2} $

  2. $\dfrac{\lambda { \mu } _{ 0 }}{2 \pi} $

  3. $\lambda { \mu } _{ 0 }$

  4. $ { \mu } _{ 0 }2\lambda \pi $

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Correct Option: A

A particle of charge $q$ and mass $m$ starts moving from origin under the action of an electric field $\vec { E }$=$E _ { 0 } \vec i $ and magnetic field $\vec { B }$=$B _ { 0 } \vec k $ . Its  velocity at $( x , 3,0 )$ is $( 4 i + 3 i )$ , the value of $x$ is:

properties of magnet magnetic field moving charges and magnetism magnetic effects of current and magnetism physics

  1. $\dfrac { 36 E _ { o } B _ { 0 } } { q m }$

  2. $\dfrac { 25 m } { 2 q E _ { 0 } }$

  3. $\dfrac { 10 m } { q E _ { o } }$

  4. $\dfrac { 25 E _ { 0 } B _ { 0 } } { m }$

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Correct Option: B
Explanation:

$\begin{array}{l} \left( { q{ \varepsilon _{ 0 } } } \right) x=\frac { 1 }{ 2 } m{ v^{ 2 } } \ \Rightarrow q{ \varepsilon _{ 0 } }x=\frac { { 25m } }{ 2 }  \ x=\frac { { 25 } }{ { 2q{ \varepsilon _{ 0 } } } }  \ Hence, \ option\, \, B\, \, is\, \, correct\, \, answer. \end{array}$

Pick correct statements from among the following : 
a) Electric field and magnetic field are basically independent
b) Electric field and magnetic field are to aspects of the electromagnetic field
c) Electric field and magnetic field may be produced by charge at rest
d) A moving charge produces both electric and magnetic fields

properties of magnet magnetic field moving charges and magnetism magnetic effects of current and magnetism physics

  1. a and b are correct

  2. b and d are correct

  3. b, c and d are correct

  4. a, c and d are correct

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Correct Option: B
Explanation:

Electric field and magnetic field are not independent. They are two aspects of the electromagnetic field. Charge at rest only produces electric field. Moving charge produces both electric field and magnetic field.

Two particles having the same specific change (q/m) enter a uniform magnetic field with the same speed but at angles of $30^ \circ$ and $60^\circ$ with the field. Let a, b and c be the ratios of their pitches, radii and periods of their helical paths respectively, then

properties of magnet magnetic field moving charges and magnetism magnetic effects of current and magnetism physics

  1. $abc = 1$

  2. $a + b = 2 \sqrt c$

  3. $a^2 = c$

  4. $ab = c$

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Correct Option: D

In a given region a charge particle is moving under the effect of electric and magnetic field with uniform velocity $\vec{v}=(\hat{i}+\hat{j}-\hat{k})$ m/s and magnetic field is given as $\vec{B}=(2\hat{i}+\hat{j}-2k)T$. The electric field is given as?

properties of magnet magnetic field moving charges and magnetism magnetic effects of current and magnetism physics

  1. $({i}+{j}-{k})$ V/m

  2. $({i}-{j}+{k})$ V/m

  3. $({i}+k)$ V/m

  4. $(-{i}-{k})$ V/m

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Correct Option: D
Explanation:

We know Force $F=qE$------(1)

and also $F=qV\times B$-----(2)
From 1 and 2 we get 
$V\times B=E$
$V\times B$=\begin{matrix} \hat { i }  & \hat { j }  & \hat { i }  \ 1 & 1 & -1 \ 2 & 1 & -2 \end{matrix}
$V\times B=(-2+1)\hat { i } -(-2+2)\hat { j } +(1-2)\hat { k } $
$V\times B==-\hat { i } -\hat { k } $

A long, straight, $non-$ conducting string, painted with a charge density of $40\mu\ c/m$, is pulled along its length at a speed of $300\ m/s$. The magnetic field at a normal distance of $5\ mm$ from the moving string is $4.8\times {10}^{-1}\ T$

properties of magnet magnetic field moving charges and magnetism magnetic effects of current and magnetism physics

  1. $4.8\times {10}^{-1}\ T$

  2. Zero

  3. $\infty$

  4. Cannot be found

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Correct Option: A

 Two concentric circular coils of $10$ turns each are situated in the same plane. Their radii are $20$ cm and $40$ cm and carry currents of $0.2$ A and $0.3$ A respectively in opposite directions. The net magnetic induction field at their common centre is 

properties of magnet magnetic field moving charges and magnetism magnetic effects of current and magnetism physics

  1. $\cfrac {35\mu _0}{4}$

  2. $\cfrac {5\mu _0}{4}$

  3. $\cfrac {7\mu _0}{8}$

  4. $\cfrac {\mu _0}{80}$

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Correct Option: B

A coil having resistance $40 \Omega$, number of turns 100 and radius 6 mm is connected to an ammeter of resistance $160 \Omega$. The coil is placed perpendicular to the magnetic field. When the coil is taken out of the field, a charge of $32 \mu C$ passes through it. The intensity of magnetic field will be

properties of magnet magnetic field moving charges and magnetism magnetic effects of current and magnetism physics

  1. 6.55 T

  2. 5.66 T

  3. 0.655 T

  4. 0.566 T

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Correct Option: D