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A proton and an alpha particle both enter a region of uniform magnetic field, B, moving at right angles to the field B. If the radius of circular orbits for both the particles is equal and the kinetic energy acquired by proton is 1 MeV, the energy acquired by the alpha particle will be :-

(A)

1 MeV

(B)

4 MeV

(C)

0.5 MeV

(D)

1.5 MeV

NEET - Medical UG-2015 Medium

Answer & Solution:

\(\large{r=radius~~of~~circular~orbit,~~v=velocity\\ F={\Large{mv^2\over r}}\Longrightarrow Bqv={\Large{mv^2\over r}}\\ v= {\Large{Bqr\over m}}\\q_\alpha=2q_a,~~~m_\alpha=4m_p\\ (K.E)_{p}={\Large{m_pv^2\over 2}}={\Large{B^2q_p^2r^2\over 2m_p}}=1~~MeV\\ (K.E)_{\alpha}={\Large{B^2q_\alpha^2r^2\over 2m_\alpha}}={\Large{B^2×4q_p^2r^2\over 2×4m_p}}={\Large{B^2q_p^2r^2\over 2m_p}}=(K.E)_p=1~~MeV }\)

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Other Questions of the same topic

Q1:

A wire carrying current I has the shape as shown in adjoining figure. Linear parts of the wire are very long and parallel to X-axis while semicircular portion of radius R is lying in Y-Z plane. Magnetic field at point O is :

(A)

\(\large \vec{B}=-\frac{\mu _{0}}{4\pi }\frac{I}{R}\left ( \pi \hat{i}-2\hat{k} \right )\)

(B)

\(\large \vec{B}=-\frac{\mu _{0}}{4\pi }\frac{I}{R}\left ( \pi \hat{i}+2\hat{k} \right )\)

(C)

\(\large \vec{B}=\frac{\mu _{0}}{4\pi }\frac{I}{R}\left ( \pi \hat{i}-2\hat{k} \right )\)

(D)

\(\large \vec{B}=\frac{\mu _{0}}{4\pi }\frac{I}{R}\left ( \pi \hat{i}+2\hat{k} \right )\)

NEET - Medical UG-2015 Hard

Q2:

Two toroids 1 and 2 have total number of turns 200 and 100 respectively with average radii 40 cm and 20 cm respectively. If they carry same current i, the ratio of the magnetic fields along the two loops is :

(A)

1 : 1

(B)

4 : 1

(C)

2 : 1

(D)

1 : 2

NEET - Medical UG-2019 Medium

Q3:

A straight conductor carrying current i splits into two parts as shown in the figure. The radius of the circular loop is R. The total magnetic field at the centre P of the loop is :

(A)

Zero

(B)

\(\large 3 \mu_0 i /32 { } R\), outward

(C)

\(\large 3 \mu_0 i /32 { } R\), inward

(D)

\(\Large \frac{ \mu_0 i}{2R}\), inward

NEET - Medical UG-2019 Medium

Q4:

A long straight wire of radius a carries a steady current I. The current is uniformly distributed over its cross - section. The ratio of the magnetic fields B and \(\large {B}'\), at a radial distances \(\large \frac{a}{2}\) and 2a respectively, from the axis of the wire is:

(A)

\(\large 4\)

(B)

\(\large \frac{1}{4}\)

(C)

\(\large \frac{1}{2}\)

(D)

\(\large 1\)

NEET - Medical UG-2016 Medium

Chemistry Biology

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