Source And Effects Of Magnetic Field | Physics JEE previous year questions with Solutions

Q 11 :
Uniform magnetic fields of different strengths ( $B_{1}$ and $B_{2}$ ) both normal to the plane of the paper exist as shown in the figure. A charged particle of mass m and charge q, at the interface at an instant, moves into the region 2 with velocity v and returns to the interface. It continues to move into region 1 and finally reaches the interface. What is the displacement of the particle during this movement along the interface?

Figure

(Consider the velocity of the particle to be normal to the magnetic field and $B_{2} > B_{1}$ ) [2025]

$\frac{m v}{q B_{1}} (1 - \frac{B_{2}}{B_{1}}) \times 2$
$\frac{m v}{q B_{1}} (1 - \frac{B_{1}}{B_{2}})$
$\frac{m v}{q B_{1}} (1 - \frac{B_{2}}{B_{1}})$
$\frac{m v}{q B_{1}} (1 - \frac{B_{1}}{B_{2}}) \times 2$

1

2

3

4

(4)

As $\vec{v}$ is $⊥$ to $\vec{B}$ , so charge particle will move in circular path, whose radius is given by

$R = \frac{m v}{q B}$

Starting point $\to A$

Ending point $\to C$

Figure

$∴$ Net displacement = AC

AC = CD – AD

$A C = \frac{2 m v}{q B_{1}} - \frac{2 m v}{q B_{2}}$

$A C = \frac{2 m v}{q B_{1}} [1 - \frac{B_{1}}{B_{2}}]$

Q 12 :
A particle of charge q, mass m and kinetic energy E enters in magnetic field perpendicular to its velocity and undergoes a circular arc of radius (r). Which of the following curves represents the variation of r with E? [2025]

Figure
Figure
Figure
Figure

1

2

3

4

(4)

Figure

$\frac{1}{2} m v^{2} = E \Rightarrow {(m v)}^{2} = 2 m E$

Also, $r = \frac{m v}{q B} \Rightarrow r = \frac{\sqrt{2 m E}}{q B}$

Figure

So, $r \infty {(E)}^{\frac{1}{2}}$

Graph should be like

Q 13 :
A proton is moving undeflected in a region of crossed electric and magnetic fields at a constant speed of $2 \times 10^{5} {ms}^{- 1}$ . When the electric field is switched off, the proton moves along a circular path of radius 2 cm. The magnitude of electric field is $x \times 10^{4} N / C$ . the value of x is ________. (Take the mass of the proton $= 1.6 \times 10^{- 27} kg$ .) [2025]

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2

For uniform speed : Bvq = Eq $\Rightarrow$ E = Bv

$r = \frac{m v}{B q} \Rightarrow B = \frac{m v}{r q}$

$E = (\frac{m v}{r q}) v = \frac{m v^{2}}{r q}$

$E = \frac{1.6 \times 10^{- 27} \times 4 \times 10^{10}}{2 \times 10^{- 2} \times 1.6 \times 10^{- 19}} = 2 \times 10^{4} N / C$

$\Rightarrow x = 2$

Q 14 :
A tightly wound long solenoid carries a current of 1.5 A. An electron is executing uniform circular motion inside the solenoid with a time period of 75 ns. The number of turns per metre in the solenoid is ________.

[Take mass of electron $m_{e} = 9 \times 10^{- 31} kg$ , charge of electron $| q_{e} | = 1.6 \times 10^{- 19} C, μ_{0} = 4 π \times 10^{- 7} \frac{N}{A^{2}}, 1 ns = 10^{- 9} s$ ] [2025]

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250

Since time period of a revolving charge is $\frac{2 π m}{q B}$

Where B = magnetic field

Due to a solenoid B = $μ_{0} n I$

$\Rightarrow \frac{2 π m}{q T} = μ_{0} n I$

$\Rightarrow n = \frac{2 π m}{q T μ_{0} I}$

$= \frac{2 π \times 9 \times 10^{- 31}}{1.6 \times 10^{- 19} \times 75 \times 10^{- 9} \times 2 \times 10^{- 7} \times 1.5}$

$\Rightarrow n = \frac{9 \times 10^{- 31}}{1.6 \times 10^{- 19} \times 75 \times 10^{- 9} \times 2 \times 10^{- 7} \times 1.5}$

$\Rightarrow n = \frac{9 \times 10^{4}}{360} = 250$ per meter

Q 15 :
A particle of charge 1.6 $μ$ C and mass 16 $μ$ g is present in a strong magnetic field of 6.28 T. The particle is then fired perpendicular to magnetic field. The time required for the particle to return to original location for the first time is __________ ms. ( $π$ = 3.14) [2025]

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10

Figure

Angle between $\vec{v}$ of charge and $\vec{B}$ is 90° motion will be uniform circular motion time period is given by

$T = \frac{2 π m}{q B} = \frac{2 π \times 16 \times 10^{- 9} kg}{1.6 \times 10^{- 6} \times 6.28}$ = 0.01 seconds

Topic Question Set

Q 12 :
A particle of charge q, mass m and kinetic energy E enters in magnetic field perpendicular to its velocity and undergoes a circular arc of radius (r). Which of the following curves represents the variation of r with E? [2025]

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Q 15 :
A particle of charge 1.6 $μ$ C and mass 16 $μ$ g is present in a strong magnetic field of 6.28 T. The particle is then fired perpendicular to magnetic field. The time required for the particle to return to original location for the first time is __________ ms. ( $π$ = 3.14) [2025]

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Topic Question Set

Q 12 : A particle of charge q, mass m and kinetic energy E enters in magnetic field perpendicular to its velocity and undergoes a circular arc of radius (r). Which of the following curves represents the variation of r with E? [2025]

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Q 15 : A particle of charge 1.6 μC and mass 16 μg is present in a strong magnetic field of 6.28 T. The particle is then fired perpendicular to magnetic field. The time required for the particle to return to original location for the first time is __________ ms. (π = 3.14) [2025]

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Q 12 :
A particle of charge q, mass m and kinetic energy E enters in magnetic field perpendicular to its velocity and undergoes a circular arc of radius (r). Which of the following curves represents the variation of r with E? [2025]

Q 15 :
A particle of charge 1.6 $μ$ C and mass 16 $μ$ g is present in a strong magnetic field of 6.28 T. The particle is then fired perpendicular to magnetic field. The time required for the particle to return to original location for the first time is __________ ms. ( $π$ = 3.14) [2025]