362788
Assertion : Time period of revolution of a charged particle in cyclotron is independent of radius and velocity. Reason : Time period of the charged particle in a cyclotron is \(T = 2\pi m/qB\).
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:
Time period of a rotating charge in a cyclotron is \(T=\dfrac{2 \pi m}{q B} . T\) is independent of \(r\) and \(v\). So option (1) is correct.
PHXII04:MOVING CHARGES AND MAGNETISM
362789
Maximum kinetic energy gained by the changed particle in the cyclotron is independent of
1 Radius of the dees
2 Charge
3 Mass
4 Frequency of revolution
Explanation:
Maximum knietic energy gained by charged particle in a cyclotron is given by \(E_{K}=\dfrac{q^{2} B^{2} R^{2}}{2 m}\) where, \(q=\) charge of the cyclotron \(B=\) intensity of magnetic field \(R=\) radius of orbit and \(m=\) mass of the particle Hence, \(E_{K}\) is independent of frequency of revolution
MHTCET - 2019
PHXII04:MOVING CHARGES AND MAGNETISM
362790
In a cyclotron, if a deuteron can gain an energy of 40\(MeV\) then a proton can gain an energy of
1 40\(MeV\)
2 80\(MeV\)
3 20\(MeV\)
4 60\(MeV\)
Explanation:
\(F=q v B=\dfrac{m v^{2}}{r}=\) Centripetal force \(E=\dfrac{1}{2} \dfrac{B^{2} q^{2} r^{2}}{m} \text { Maximum energy, }\) Hence, ratio of energy of deuteron and proton is \(\begin{aligned}& \dfrac{E_{d}}{E_{p}}=\left(\dfrac{q_{d}}{q_{p}}\right)^{2}\left(\dfrac{m_{p}}{m_{d}}\right) \\& \dfrac{40}{E_{p}}=\left(\dfrac{q}{q}\right)^{2}\left(\dfrac{m}{2 m}\right) \Rightarrow E_{p}=80 \mathrm{MeV}\end{aligned}\)
PHXII04:MOVING CHARGES AND MAGNETISM
362791
In a cyclotron, if the frequency of proton is \(5MHz\), the magnetic field strength necessary for resonance is
1 2.32\(T\)
2 0.528\(T\)
3 0.32\(T\)
4 0.398\(T\)
Explanation:
To have resonance in cyclotron the frequency \(f = \frac{{Bq}}{{2\pi m}} \Rightarrow B = \frac{{2\pi mf}}{q}\) \( = \frac{{2 \times 3.14 \times 1.67 \times {{10}^{ - 27}} \times 5 \times {{10}^6}}}{{1.6 \times {{10}^{ - 19}}}} = 0.32\,T\)
362788
Assertion : Time period of revolution of a charged particle in cyclotron is independent of radius and velocity. Reason : Time period of the charged particle in a cyclotron is \(T = 2\pi m/qB\).
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:
Time period of a rotating charge in a cyclotron is \(T=\dfrac{2 \pi m}{q B} . T\) is independent of \(r\) and \(v\). So option (1) is correct.
PHXII04:MOVING CHARGES AND MAGNETISM
362789
Maximum kinetic energy gained by the changed particle in the cyclotron is independent of
1 Radius of the dees
2 Charge
3 Mass
4 Frequency of revolution
Explanation:
Maximum knietic energy gained by charged particle in a cyclotron is given by \(E_{K}=\dfrac{q^{2} B^{2} R^{2}}{2 m}\) where, \(q=\) charge of the cyclotron \(B=\) intensity of magnetic field \(R=\) radius of orbit and \(m=\) mass of the particle Hence, \(E_{K}\) is independent of frequency of revolution
MHTCET - 2019
PHXII04:MOVING CHARGES AND MAGNETISM
362790
In a cyclotron, if a deuteron can gain an energy of 40\(MeV\) then a proton can gain an energy of
1 40\(MeV\)
2 80\(MeV\)
3 20\(MeV\)
4 60\(MeV\)
Explanation:
\(F=q v B=\dfrac{m v^{2}}{r}=\) Centripetal force \(E=\dfrac{1}{2} \dfrac{B^{2} q^{2} r^{2}}{m} \text { Maximum energy, }\) Hence, ratio of energy of deuteron and proton is \(\begin{aligned}& \dfrac{E_{d}}{E_{p}}=\left(\dfrac{q_{d}}{q_{p}}\right)^{2}\left(\dfrac{m_{p}}{m_{d}}\right) \\& \dfrac{40}{E_{p}}=\left(\dfrac{q}{q}\right)^{2}\left(\dfrac{m}{2 m}\right) \Rightarrow E_{p}=80 \mathrm{MeV}\end{aligned}\)
PHXII04:MOVING CHARGES AND MAGNETISM
362791
In a cyclotron, if the frequency of proton is \(5MHz\), the magnetic field strength necessary for resonance is
1 2.32\(T\)
2 0.528\(T\)
3 0.32\(T\)
4 0.398\(T\)
Explanation:
To have resonance in cyclotron the frequency \(f = \frac{{Bq}}{{2\pi m}} \Rightarrow B = \frac{{2\pi mf}}{q}\) \( = \frac{{2 \times 3.14 \times 1.67 \times {{10}^{ - 27}} \times 5 \times {{10}^6}}}{{1.6 \times {{10}^{ - 19}}}} = 0.32\,T\)
362788
Assertion : Time period of revolution of a charged particle in cyclotron is independent of radius and velocity. Reason : Time period of the charged particle in a cyclotron is \(T = 2\pi m/qB\).
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:
Time period of a rotating charge in a cyclotron is \(T=\dfrac{2 \pi m}{q B} . T\) is independent of \(r\) and \(v\). So option (1) is correct.
PHXII04:MOVING CHARGES AND MAGNETISM
362789
Maximum kinetic energy gained by the changed particle in the cyclotron is independent of
1 Radius of the dees
2 Charge
3 Mass
4 Frequency of revolution
Explanation:
Maximum knietic energy gained by charged particle in a cyclotron is given by \(E_{K}=\dfrac{q^{2} B^{2} R^{2}}{2 m}\) where, \(q=\) charge of the cyclotron \(B=\) intensity of magnetic field \(R=\) radius of orbit and \(m=\) mass of the particle Hence, \(E_{K}\) is independent of frequency of revolution
MHTCET - 2019
PHXII04:MOVING CHARGES AND MAGNETISM
362790
In a cyclotron, if a deuteron can gain an energy of 40\(MeV\) then a proton can gain an energy of
1 40\(MeV\)
2 80\(MeV\)
3 20\(MeV\)
4 60\(MeV\)
Explanation:
\(F=q v B=\dfrac{m v^{2}}{r}=\) Centripetal force \(E=\dfrac{1}{2} \dfrac{B^{2} q^{2} r^{2}}{m} \text { Maximum energy, }\) Hence, ratio of energy of deuteron and proton is \(\begin{aligned}& \dfrac{E_{d}}{E_{p}}=\left(\dfrac{q_{d}}{q_{p}}\right)^{2}\left(\dfrac{m_{p}}{m_{d}}\right) \\& \dfrac{40}{E_{p}}=\left(\dfrac{q}{q}\right)^{2}\left(\dfrac{m}{2 m}\right) \Rightarrow E_{p}=80 \mathrm{MeV}\end{aligned}\)
PHXII04:MOVING CHARGES AND MAGNETISM
362791
In a cyclotron, if the frequency of proton is \(5MHz\), the magnetic field strength necessary for resonance is
1 2.32\(T\)
2 0.528\(T\)
3 0.32\(T\)
4 0.398\(T\)
Explanation:
To have resonance in cyclotron the frequency \(f = \frac{{Bq}}{{2\pi m}} \Rightarrow B = \frac{{2\pi mf}}{q}\) \( = \frac{{2 \times 3.14 \times 1.67 \times {{10}^{ - 27}} \times 5 \times {{10}^6}}}{{1.6 \times {{10}^{ - 19}}}} = 0.32\,T\)
362788
Assertion : Time period of revolution of a charged particle in cyclotron is independent of radius and velocity. Reason : Time period of the charged particle in a cyclotron is \(T = 2\pi m/qB\).
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:
Time period of a rotating charge in a cyclotron is \(T=\dfrac{2 \pi m}{q B} . T\) is independent of \(r\) and \(v\). So option (1) is correct.
PHXII04:MOVING CHARGES AND MAGNETISM
362789
Maximum kinetic energy gained by the changed particle in the cyclotron is independent of
1 Radius of the dees
2 Charge
3 Mass
4 Frequency of revolution
Explanation:
Maximum knietic energy gained by charged particle in a cyclotron is given by \(E_{K}=\dfrac{q^{2} B^{2} R^{2}}{2 m}\) where, \(q=\) charge of the cyclotron \(B=\) intensity of magnetic field \(R=\) radius of orbit and \(m=\) mass of the particle Hence, \(E_{K}\) is independent of frequency of revolution
MHTCET - 2019
PHXII04:MOVING CHARGES AND MAGNETISM
362790
In a cyclotron, if a deuteron can gain an energy of 40\(MeV\) then a proton can gain an energy of
1 40\(MeV\)
2 80\(MeV\)
3 20\(MeV\)
4 60\(MeV\)
Explanation:
\(F=q v B=\dfrac{m v^{2}}{r}=\) Centripetal force \(E=\dfrac{1}{2} \dfrac{B^{2} q^{2} r^{2}}{m} \text { Maximum energy, }\) Hence, ratio of energy of deuteron and proton is \(\begin{aligned}& \dfrac{E_{d}}{E_{p}}=\left(\dfrac{q_{d}}{q_{p}}\right)^{2}\left(\dfrac{m_{p}}{m_{d}}\right) \\& \dfrac{40}{E_{p}}=\left(\dfrac{q}{q}\right)^{2}\left(\dfrac{m}{2 m}\right) \Rightarrow E_{p}=80 \mathrm{MeV}\end{aligned}\)
PHXII04:MOVING CHARGES AND MAGNETISM
362791
In a cyclotron, if the frequency of proton is \(5MHz\), the magnetic field strength necessary for resonance is
1 2.32\(T\)
2 0.528\(T\)
3 0.32\(T\)
4 0.398\(T\)
Explanation:
To have resonance in cyclotron the frequency \(f = \frac{{Bq}}{{2\pi m}} \Rightarrow B = \frac{{2\pi mf}}{q}\) \( = \frac{{2 \times 3.14 \times 1.67 \times {{10}^{ - 27}} \times 5 \times {{10}^6}}}{{1.6 \times {{10}^{ - 19}}}} = 0.32\,T\)
