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PHXII04:MOVING CHARGES AND MAGNETISM

362792 In cyclotron, for a given magnet, radius of the semicircle traced by positive ion is directly proportional to ( $v =$ velocity of positive ion)

1

v^{- 2}

2

v^{- 1}

3

v

4

v^{2}

Explanation:

In cyclotron,
$∴ B q v = \frac{m v^{2}}{r}$
$\Rightarrow r = \frac{m v}{B q} \Rightarrow r α v$ ( $B =$ Constant)

PHXII04:MOVING CHARGES AND MAGNETISM

362793 Assertion :
Any ion cannot move with a speed beyond a certain limit in a cyclotron.
Reason :
As velocity increases time taken by ion increases.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

In non-relativistic regime $(M v^{2} / R) = Q v B \Rightarrow v_{max} = \frac{Q B R}{M}$
Where $R$ is radius of Dees of cyclotron. In a cyclotron, the time for an ion to complete one revolution is independent of its velocity due to an alternating electric field with some frequency $f_{supply}$ .
$T = \frac{2 π M}{Q B}$
However, as ions approach the speed of light, relativistic effects limit further acceleration. So correct option is (3).

PHXII04:MOVING CHARGES AND MAGNETISM

362794 Cyclotron is adjusted to give proton beam, magnetic induction is $0.15 w b m^{- 2}$ and the extreme radius is 1.5 $m$ . The energy of emergent proton in $M e V$ will be

1 2.43

2 24.3

3 34.2

4 3.42

Explanation:

Radius of circular path traced by moving charged particle in uniform magnetic field
$r = \frac{m v}{B q}$
$∴ V_{max} = \frac{B q r_{max}}{m}$
The maximum $K E$ that it can get in cyclotron
$\begin{matrix} = k_{max} = \frac{1}{2} m {(V_{max})}^{2} \\ k_{max} = \frac{1}{2} m {(\frac{B q r_{max}}{m})}^{2} = \frac{B^{2} q^{2} r_{max}^{2}}{2 m} = 2.4 MeV \end{matrix}$

PHXII04:MOVING CHARGES AND MAGNETISM

362795 Assertion :
Cyclotron is a device which is used to accelerate charged particles.
Reason :
Cyclotron frequency depends upon the velocity.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$f = \frac{q B}{2 π m} = \frac{1}{T} \Rightarrow$ Reason is false Cyclotrons accelerate charged particles using magnetic and electric fields. The assertion is true. So correct option is (3).

PHXII04:MOVING CHARGES AND MAGNETISM

362792 In cyclotron, for a given magnet, radius of the semicircle traced by positive ion is directly proportional to ( $v =$ velocity of positive ion)

1

v^{- 2}

2

v^{- 1}

3

v

4

v^{2}

Explanation:

In cyclotron,
$∴ B q v = \frac{m v^{2}}{r}$
$\Rightarrow r = \frac{m v}{B q} \Rightarrow r α v$ ( $B =$ Constant)

PHXII04:MOVING CHARGES AND MAGNETISM

362793 Assertion :
Any ion cannot move with a speed beyond a certain limit in a cyclotron.
Reason :
As velocity increases time taken by ion increases.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

In non-relativistic regime $(M v^{2} / R) = Q v B \Rightarrow v_{max} = \frac{Q B R}{M}$
Where $R$ is radius of Dees of cyclotron. In a cyclotron, the time for an ion to complete one revolution is independent of its velocity due to an alternating electric field with some frequency $f_{supply}$ .
$T = \frac{2 π M}{Q B}$
However, as ions approach the speed of light, relativistic effects limit further acceleration. So correct option is (3).

PHXII04:MOVING CHARGES AND MAGNETISM

362794 Cyclotron is adjusted to give proton beam, magnetic induction is $0.15 w b m^{- 2}$ and the extreme radius is 1.5 $m$ . The energy of emergent proton in $M e V$ will be

1 2.43

2 24.3

3 34.2

4 3.42

Explanation:

Radius of circular path traced by moving charged particle in uniform magnetic field
$r = \frac{m v}{B q}$
$∴ V_{max} = \frac{B q r_{max}}{m}$
The maximum $K E$ that it can get in cyclotron
$\begin{matrix} = k_{max} = \frac{1}{2} m {(V_{max})}^{2} \\ k_{max} = \frac{1}{2} m {(\frac{B q r_{max}}{m})}^{2} = \frac{B^{2} q^{2} r_{max}^{2}}{2 m} = 2.4 MeV \end{matrix}$

PHXII04:MOVING CHARGES AND MAGNETISM

362795 Assertion :
Cyclotron is a device which is used to accelerate charged particles.
Reason :
Cyclotron frequency depends upon the velocity.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$f = \frac{q B}{2 π m} = \frac{1}{T} \Rightarrow$ Reason is false Cyclotrons accelerate charged particles using magnetic and electric fields. The assertion is true. So correct option is (3).

PHXII04:MOVING CHARGES AND MAGNETISM

362792 In cyclotron, for a given magnet, radius of the semicircle traced by positive ion is directly proportional to ( $v =$ velocity of positive ion)

1

v^{- 2}

2

v^{- 1}

3

v

4

v^{2}

Explanation:

In cyclotron,
$∴ B q v = \frac{m v^{2}}{r}$
$\Rightarrow r = \frac{m v}{B q} \Rightarrow r α v$ ( $B =$ Constant)

PHXII04:MOVING CHARGES AND MAGNETISM

362793 Assertion :
Any ion cannot move with a speed beyond a certain limit in a cyclotron.
Reason :
As velocity increases time taken by ion increases.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

In non-relativistic regime $(M v^{2} / R) = Q v B \Rightarrow v_{max} = \frac{Q B R}{M}$
Where $R$ is radius of Dees of cyclotron. In a cyclotron, the time for an ion to complete one revolution is independent of its velocity due to an alternating electric field with some frequency $f_{supply}$ .
$T = \frac{2 π M}{Q B}$
However, as ions approach the speed of light, relativistic effects limit further acceleration. So correct option is (3).

PHXII04:MOVING CHARGES AND MAGNETISM

362794 Cyclotron is adjusted to give proton beam, magnetic induction is $0.15 w b m^{- 2}$ and the extreme radius is 1.5 $m$ . The energy of emergent proton in $M e V$ will be

1 2.43

2 24.3

3 34.2

4 3.42

Explanation:

Radius of circular path traced by moving charged particle in uniform magnetic field
$r = \frac{m v}{B q}$
$∴ V_{max} = \frac{B q r_{max}}{m}$
The maximum $K E$ that it can get in cyclotron
$\begin{matrix} = k_{max} = \frac{1}{2} m {(V_{max})}^{2} \\ k_{max} = \frac{1}{2} m {(\frac{B q r_{max}}{m})}^{2} = \frac{B^{2} q^{2} r_{max}^{2}}{2 m} = 2.4 MeV \end{matrix}$

PHXII04:MOVING CHARGES AND MAGNETISM

362795 Assertion :
Cyclotron is a device which is used to accelerate charged particles.
Reason :
Cyclotron frequency depends upon the velocity.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$f = \frac{q B}{2 π m} = \frac{1}{T} \Rightarrow$ Reason is false Cyclotrons accelerate charged particles using magnetic and electric fields. The assertion is true. So correct option is (3).

PHXII04:MOVING CHARGES AND MAGNETISM

362792 In cyclotron, for a given magnet, radius of the semicircle traced by positive ion is directly proportional to ( $v =$ velocity of positive ion)

1

v^{- 2}

2

v^{- 1}

3

v

4

v^{2}

Explanation:

In cyclotron,
$∴ B q v = \frac{m v^{2}}{r}$
$\Rightarrow r = \frac{m v}{B q} \Rightarrow r α v$ ( $B =$ Constant)

PHXII04:MOVING CHARGES AND MAGNETISM

362793 Assertion :
Any ion cannot move with a speed beyond a certain limit in a cyclotron.
Reason :
As velocity increases time taken by ion increases.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

In non-relativistic regime $(M v^{2} / R) = Q v B \Rightarrow v_{max} = \frac{Q B R}{M}$
Where $R$ is radius of Dees of cyclotron. In a cyclotron, the time for an ion to complete one revolution is independent of its velocity due to an alternating electric field with some frequency $f_{supply}$ .
$T = \frac{2 π M}{Q B}$
However, as ions approach the speed of light, relativistic effects limit further acceleration. So correct option is (3).

PHXII04:MOVING CHARGES AND MAGNETISM

362794 Cyclotron is adjusted to give proton beam, magnetic induction is $0.15 w b m^{- 2}$ and the extreme radius is 1.5 $m$ . The energy of emergent proton in $M e V$ will be

1 2.43

2 24.3

3 34.2

4 3.42

Explanation:

Radius of circular path traced by moving charged particle in uniform magnetic field
$r = \frac{m v}{B q}$
$∴ V_{max} = \frac{B q r_{max}}{m}$
The maximum $K E$ that it can get in cyclotron
$\begin{matrix} = k_{max} = \frac{1}{2} m {(V_{max})}^{2} \\ k_{max} = \frac{1}{2} m {(\frac{B q r_{max}}{m})}^{2} = \frac{B^{2} q^{2} r_{max}^{2}}{2 m} = 2.4 MeV \end{matrix}$

PHXII04:MOVING CHARGES AND MAGNETISM

362795 Assertion :
Cyclotron is a device which is used to accelerate charged particles.
Reason :
Cyclotron frequency depends upon the velocity.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$f = \frac{q B}{2 π m} = \frac{1}{T} \Rightarrow$ Reason is false Cyclotrons accelerate charged particles using magnetic and electric fields. The assertion is true. So correct option is (3).