Tag: moving charges and magnetism

Quizzes (9) Questions (79)

Questions Related to moving charges and magnetism

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

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

  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 } $
Reveal answer Fill a bubble to check yourself
A Correct answer
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

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

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

  1. 1 : 2

  2. 1 : 4

  3. 2 : 1

  4. 4 : 1
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The magnetic field due to an infinitely long straight current-carrying wire is inversely proportional to the distance r from the wire (B proportional to 1/r). Therefore, the ratio of the magnetic fields at 10 cm and 20 cm is B1/B2 = r2/r1 = 20/10 = 2:1.

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

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

  1. $\dfrac{\lambda { \mu } _{ 0 }}{2} $
  2. $\dfrac{\lambda { \mu } _{ 0 }}{2 \pi} $
  3. $\lambda { \mu } _{ 0 }$
  4. $ { \mu } _{ 0 }2\lambda \pi $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For an infinite current sheet with current per unit length lambda, the magnetic field is B = mu0 * lambda / 2.

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

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:

  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. $\dfrac { 25 E _ { 0 } B _ { 0 } } { m }$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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

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

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

  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
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

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

  1. $abc = 1$
  2. $a + b = 2 \sqrt c$
  3. $a^2 = c$
  4. $ab = c$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Pitch p = (2 * pi * m * v * cos(theta)) / (q * B), radius r = (m * v * sin(theta)) / (q * B), period T = (2 * pi * m) / (q * B). Ratios: a = p1/p2 = cos(30)/cos(60) = sqrt(3), b = r1/r2 = sin(30)/sin(60) = 1/sqrt(3), c = T1/T2 = 1. Thus, a * b = sqrt(3) * (1/sqrt(3)) = 1, and c = 1. So a * b = c.

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

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?

  1. $({i}+{j}-{k})$ V/m
  2. $({i}-{j}+{k})$ V/m
  3. $({i}+k)$ V/m
  4. $(-{i}-{k})$ V/m
Reveal answer Fill a bubble to check yourself
D Correct answer
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 } $

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

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 $4.8\times {10}^{-1}\ T$

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

  2. Zero
  3. $\infty$

  4. Cannot be found
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A moving charged string is equivalent to a current I = lambda * v. Here, lambda = 40 * 10^-6 C/m, v = 300 m/s, so I = 40 * 10^-6 * 300 = 12 * 10^-3 A. B = mu0 * I / (2 * pi * r) = (2 * 10^-7 * 12 * 10^-3) / (5 * 10^-3) = 4.8 * 10^-7 T. The value in the question is 4.8 * 10^-1 T, which is incorrect.

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

 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 

  1. $\cfrac {35\mu _0}{4}$
  2. $\cfrac {5\mu _0}{4}$
  3. $\cfrac {7\mu _0}{8}$
  4. $\cfrac {\mu _0}{80}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The magnetic field at the center of a circular coil is B = (mu_0 * N * I) / (2 * R). For two coils with opposite currents, the net field is the difference between the two fields: B_net = (mu_0 * 10 / 2) * |(0.2 / 0.2) - (0.3 / 0.4)| = 5 * mu_0 * |1 - 0.75| = 5 * mu_0 * 0.25 = 1.25 * mu_0 = 5 * mu_0 / 4.

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

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

  1. 6.55 T

  2. 5.66 T

  3. 0.655 T

  4. 0.566 T
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The total resistance in the circuit is R_total = 40 + 160 = 200 ohms. The charge passed is q = delta_phi / R_total, where delta_phi = N * B * A. Given q = 32 * 10^-6 C, N = 100, A = pi * (0.006)^2, we solve for B: B = (q * R_total) / (N * A) = (32 * 10^-6 * 200) / (100 * pi * 36 * 10^-6) = 64 / (36 * pi) approx 0.566 T.