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, \(\therefore B q v=\dfrac{m v^{2}}{r}\) \( \Rightarrow r = \frac{{mv}}{{Bq}} \Rightarrow r\alpha v\) (\(B=\) 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\(\left(M v^{2} / R\right)=Q v B \Rightarrow v_{\max }=\dfrac{Q B R}{M}\) 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 \(f_{\text {supply }}\). \(T=\dfrac{2 \pi M}{Q B}\) 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 \(0.15wb{m^{ - 2}}\) and the extreme radius is 1.5\(m\). The energy of emergent proton in \(MeV\) 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 \(r=\dfrac{m v}{B q}\) \(\therefore V_{\max }=\dfrac{B q r_{\max }}{m}\) The maximum \(KE\) that it can get in cyclotron \(\begin{gathered}=k_{\max }=\dfrac{1}{2} m\left(V_{\max }\right)^{2} \\k_{\text {max }}=\dfrac{1}{2} m\left(\dfrac{B q r_{\max }}{m}\right)^{2}=\dfrac{B^{2} q^{2} r_{\max }^{2}}{2 m}=2.4 \mathrm{MeV}\end{gathered}\)
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:
\(f=\dfrac{q B}{2 \pi m}=\dfrac{1}{T} \Rightarrow\) Reason is false Cyclotrons accelerate charged particles using magnetic and electric fields. The assertion is true. So correct option is (3).
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, \(\therefore B q v=\dfrac{m v^{2}}{r}\) \( \Rightarrow r = \frac{{mv}}{{Bq}} \Rightarrow r\alpha v\) (\(B=\) 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\(\left(M v^{2} / R\right)=Q v B \Rightarrow v_{\max }=\dfrac{Q B R}{M}\) 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 \(f_{\text {supply }}\). \(T=\dfrac{2 \pi M}{Q B}\) 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 \(0.15wb{m^{ - 2}}\) and the extreme radius is 1.5\(m\). The energy of emergent proton in \(MeV\) 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 \(r=\dfrac{m v}{B q}\) \(\therefore V_{\max }=\dfrac{B q r_{\max }}{m}\) The maximum \(KE\) that it can get in cyclotron \(\begin{gathered}=k_{\max }=\dfrac{1}{2} m\left(V_{\max }\right)^{2} \\k_{\text {max }}=\dfrac{1}{2} m\left(\dfrac{B q r_{\max }}{m}\right)^{2}=\dfrac{B^{2} q^{2} r_{\max }^{2}}{2 m}=2.4 \mathrm{MeV}\end{gathered}\)
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:
\(f=\dfrac{q B}{2 \pi m}=\dfrac{1}{T} \Rightarrow\) Reason is false Cyclotrons accelerate charged particles using magnetic and electric fields. The assertion is true. So correct option is (3).
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, \(\therefore B q v=\dfrac{m v^{2}}{r}\) \( \Rightarrow r = \frac{{mv}}{{Bq}} \Rightarrow r\alpha v\) (\(B=\) 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\(\left(M v^{2} / R\right)=Q v B \Rightarrow v_{\max }=\dfrac{Q B R}{M}\) 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 \(f_{\text {supply }}\). \(T=\dfrac{2 \pi M}{Q B}\) 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 \(0.15wb{m^{ - 2}}\) and the extreme radius is 1.5\(m\). The energy of emergent proton in \(MeV\) 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 \(r=\dfrac{m v}{B q}\) \(\therefore V_{\max }=\dfrac{B q r_{\max }}{m}\) The maximum \(KE\) that it can get in cyclotron \(\begin{gathered}=k_{\max }=\dfrac{1}{2} m\left(V_{\max }\right)^{2} \\k_{\text {max }}=\dfrac{1}{2} m\left(\dfrac{B q r_{\max }}{m}\right)^{2}=\dfrac{B^{2} q^{2} r_{\max }^{2}}{2 m}=2.4 \mathrm{MeV}\end{gathered}\)
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:
\(f=\dfrac{q B}{2 \pi m}=\dfrac{1}{T} \Rightarrow\) Reason is false Cyclotrons accelerate charged particles using magnetic and electric fields. The assertion is true. So correct option is (3).
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, \(\therefore B q v=\dfrac{m v^{2}}{r}\) \( \Rightarrow r = \frac{{mv}}{{Bq}} \Rightarrow r\alpha v\) (\(B=\) 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\(\left(M v^{2} / R\right)=Q v B \Rightarrow v_{\max }=\dfrac{Q B R}{M}\) 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 \(f_{\text {supply }}\). \(T=\dfrac{2 \pi M}{Q B}\) 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 \(0.15wb{m^{ - 2}}\) and the extreme radius is 1.5\(m\). The energy of emergent proton in \(MeV\) 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 \(r=\dfrac{m v}{B q}\) \(\therefore V_{\max }=\dfrac{B q r_{\max }}{m}\) The maximum \(KE\) that it can get in cyclotron \(\begin{gathered}=k_{\max }=\dfrac{1}{2} m\left(V_{\max }\right)^{2} \\k_{\text {max }}=\dfrac{1}{2} m\left(\dfrac{B q r_{\max }}{m}\right)^{2}=\dfrac{B^{2} q^{2} r_{\max }^{2}}{2 m}=2.4 \mathrm{MeV}\end{gathered}\)
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:
\(f=\dfrac{q B}{2 \pi m}=\dfrac{1}{T} \Rightarrow\) Reason is false Cyclotrons accelerate charged particles using magnetic and electric fields. The assertion is true. So correct option is (3).
