Tag: magnetic flux density

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Questions Related to magnetic flux density

Multiple choice physics magnetic fields and electromagnetism magnetic flux density magnetic flux electromagnetic induction

A square loop of side 12 cm and resistance 0.60$\Omega$ is placed vertically in the east-west plane. A uniform magnetic field of 0.1 T is setup across the plane in north-east direction. The magnetic field is decreased to zero in 0.6 s at a steady rate. The magnitude of current during this time interval is

  1. $1.42 \times 10^{-3} A$
  2. $2.67 \times 10^{-3} A$
  3. $3.41\times 10^{-3} A$
  4. $4.21 \times 10^{-3} A$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Here, Area $A=l^2=(12cm)^2=1.4\times 10^{-2} m^2$
$R=0.60\omega, B _1=0.10 T,\theta=45^0$
$B _2=0,dt=0.6$ s
Initial flux,
$\phi _1=B _1Acos\theta$
      $=0.10\times1.4\times10^{-2}\times cos 45^0$
      $=9.8\times 10^{-4}$

final flux, $\phi _2$=0
Induced emf,$E=\dfrac{| d\phi |}{dt}=\dfrac{|\phi _2-\phi _1|}{dt}$
                      $E=\dfrac{|9.8\times 10^{-4}|}{0.6}s\\,\,\,\,\,=1.6\times10^{-3}V$
Current, $I=\dfrac{E}{R}=\dfrac{1.6\times\times 10^{-3}}{0.6}=2.67 \times 10^{-3}$

Multiple choice physics magnetic fields and electromagnetism magnetic flux density magnetic flux electromagnetic induction

When the normal to a coil points in the direction of magnetic field (B), then flux is 

  1. a scalar quantity

  2. a vector quantity

  3. neither scalar nor vector

  4. uncertain
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Dot product of field and area vectors is flux . $\Phi=B.dS$, and we know dot product of two vectors is a scalar quantity.
Therefore, flux is scalar.

Multiple choice physics magnetic fields and electromagnetism magnetic flux density magnetic flux electromagnetic induction

Current $i _0$ is being carried by an infinite wire passing through origin along the direction $\hat{i} + \hat{j} + \hat{k}$. Find magnetic field due to the wire at point $(1 m, 0, 0)$.

  1. $\dfrac{(\mu _0 i)}{(2 \pi)} T$
  2. $\dfrac{(\mu _0 i)}{(\sqrt{2} \pi)} T$
  3. $\dfrac{(\mu _0 i)}{(4 \pi)} T$
  4. $\dfrac{(\sqrt{3} \mu _0 i)}{(2 \sqrt{2} \pi)} T$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The magnetic field B = (mu_0 * i) / (2 * pi * r). The distance r from the wire (passing through origin along 1,1,1) to (1,0,0) is the perpendicular distance. Using the cross product formula for distance from a point to a line, r = |(r_p - r_0) x u| = |(1,0,0) x (1/sqrt(3), 1/sqrt(3), 1/sqrt(3))| = |(0, -1/sqrt(3), 1/sqrt(3))| = sqrt(2/3). B = (mu_0 * i) / (2 * pi * sqrt(2/3)) = (sqrt(3) * mu_0 * i) / (2 * sqrt(2) * pi).

Multiple choice physics magnetic fields and electromagnetism magnetic flux density magnetic flux electromagnetic induction

A charge q is placed at the centre of a cylinder of radius R and length 2R. Then electric flux through the curved surface of the cylinder is 

  1. $\cfrac { q }{ 2 { \epsilon } _{ 0 } } $
  2. $\cfrac { q }{ 4 { \epsilon } _{ 0 } } $
  3. $\cfrac { q }{ \sqrt { 2 } { \epsilon } _{ 0 } } $
  4. $\cfrac { q }{ 2\sqrt { 2 } { \epsilon } _{ 0 } } $
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice physics magnetic fields and electromagnetism magnetic flux density magnetic flux electromagnetic induction

A cyclotron in which protons are accelerated has a flux density 1.57T. The variation of frequency of electric field is (in Hz) 

  1. $4.8 \times 10 ^ { 8 }$
  2. $8.4 \times 10 ^ { 8 }$
  3. $2.5 \times 10 ^ { 7 }$
  4. $4.8 \times 10 ^ { 6 }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Cyclotron frequency f = qB / (2 * pi * m). For protons, q = 1.6e-19 C, m = 1.67e-27 kg, B = 1.57 T. f = (1.6e-19 * 1.57) / (2 * 3.14 * 1.67e-27) approx 2.4e7 Hz.

Multiple choice physics magnetic fields and electromagnetism magnetic flux density magnetic flux electromagnetic induction

Current in a circular coil having negligible resistance and inductance 0.1 H is increasing at the rate of $1 As^{-1}$. The power generated in the coil when the magnetic flux linked with it is 0.1 Wb will be:-

  1. 0.05 W

  2. 0.1W

  3. 1 W

  4. 10 W
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Induced EMF e = -L * (di/dt) = -0.1 * 1 = -0.1 V. Power P = e * i. The current i = flux / L = 0.1 / 0.1 = 1 A. P = 0.1 * 1 = 0.1 W.