12. ⇒ (AIPMT 2009)

The magnetic force acting on a charged particle of charge $-$ 2 $μ$ C in a magnetic frield of 2 T acting in y direction, when the particle velocity is $(2 \hat{i} + 3 \hat{j}) \times 10^{6} m s^{- 1}$

A. 4 N in z direction

B. 8 N in y direction

C. 8 N in z direction

D. 8 N in $-$ z direction

Correct Answer is Option (D)

The magnetic force acting on the charged paraticle is given by

$\vec{F} = q (\vec{v} \times \vec{B})$

$= (- 2 \times 10^{- 6}) [{(2 \hat{i} + 3 \hat{j}) \times 10^{6}} \times (2 \hat{j})]$

$= - 4 (2 \hat{k})$

$= - 8 \hat{k}$

$∴$ Force is of 8N along – z-axis.

13. ⇒ (AIPMT 2009)

Under the influence of a uniform magnetic field, a charged particle moves with constant speed v in a circle of radius R. The time period of rotation of the particle

A. depends on R and not on v

B. is independent of both v and R

C. depends on both v and R

D. depends on v and not on R

Correct Answer is Option (B)

For the circular motion in a cyclotron,

$q v B = \frac{m v^{2}}{r} \Rightarrow q B = m ω = \frac{m \times 2 π}{T}$

$∴ T = \frac{2 π m}{q B}$ is independent of v and r.

14. ⇒ (AIPMT 2008)

A particle of mass m, charge Q and kinetic energy T enters a transverse uniform magnetic field of induction $\vec{B}$ . After 3 seconds the kinetic energy of the particle will be

A. T

B. 4T

C. 3T

D. 2T

Correct Answer is Option (A)

When a charged particle having a given K.E., T enters in a field of magnetic induction, which is perpendicular to its velocity, it takes a circular trajectory. It does not increase in energy, therefore T is the K.E.

15. ⇒ (AIPMT 2007)

Under the influence of a uniform magnetic field, a charged particle moves with constant speed v in a circle of radius R. The time period of rotation of the particle

A. depends on R and not on v

B. is independent of both v and R

C. depends on both v and R

D. depends on v and not on R

Correct Answer is Option (B)

For the circular motion in a cyclotron,

$q v B = \frac{m v^{2}}{r} \Rightarrow q B = m ω = \frac{m \times 2 π}{T}$

$∴ T = \frac{2 π m}{q B}$ is independent of v and r.

16. ⇒ (AIPMT 2006)

When a charged particle moving with velocity $\vec{v}$ is subjected to a magnetic field of induction $\vec{B}$ , the force on it is non-zero. This implies that

A. angle between is either zero or 180^o

B. angle between is necessarily 90^o

C. angle between can have any value other than 90^o

D. angle between can have any value other than zero and 180^o.

Correct Answer is Option (D)

Force on a particle moving with velocity $\vec{v}$ in a magnetic field $\vec{B}$ is

$\vec{F} = q (\vec{v} \times \vec{B})$

$\Rightarrow$ F = qvBsin $θ$

(i) When $θ$ = 0°, F = qvBsin0° = 0

(ii) When $θ$ = 90°, F = qvBsin90° = qvB

(iii) When $θ$ = 180°, F = qvBsin180° = 0

If angle between v and B is either zero or 180º, then value of F will be zero.

17. ⇒ (AIPMT 2005)

An electron moves in a circular orbit with a uniform speed v. It producess a magnetic field B at the centre of the circle. The radius of the circle is proportional to

A. $\sqrt{B / v}$

B. $B / v$

C. $\sqrt{v / B}$

D. $v / B$

Correct Answer is Option (C)

The magnetic field produce by moving electron in circular path

B = $\frac{μ_{0} i}{2 r}$

and i = $\frac{q}{2 π r} \times v$

$∴$ B = $\frac{μ_{0} q v}{4 π r^{2}}$

$\Rightarrow$ r $\propto$ $\sqrt{\frac{v}{B}}$

18. ⇒ ( AIPMT 2005)

A very long straight wire carries a current $I$ . At the instant when a charge +Q at point P has velocity $\vec{v}$ , as shown, the force on the charge is

AIPMT 2005 Physics - Moving Charges and Magnetism Question 29 English

A. along Oy

B. opposite to Oy

C. along Ox

D. opposite to Ox

Correct Answer is Option (A)

The direction of $\vec{B}$ is due to i is acting inwards i.e. into the paper along $(- \hat{k})$ .

$∴$ The magnetic force

$\vec{F} = Q (\vec{v} \times \vec{B}) = Q (\vec{v} \hat{i}) \times B (- \hat{k}) = Q v B \hat{j}$

So, $\vec{F}$ is along Oy direction.

19. ⇒ (AIPMT 2003)

A charged particle moves through a magnetic field in a firection perpendicular to it. Then the

A. speed of the particle remains unchanged

B. direction of the particle remains unchanged

C. acceleration remains unchanged

D. velocity remains unchanged

Correct Answer is Option (A)

If a moving charged particle is subjected to a perpendicular uniform magnetic field, then according to F = qvB sin $θ$ , it will experience a maximum force which will provide the centripetal force to particle and it will describe a circular path with uniform speed.

20. ⇒ (AIPMT 2002)

To convert a galvanometer into a voltmeter one should connect a

A. high resistance in series with galvanometer

B. low resistance in series with galvanometer

C. high resistance in parallel with galvanometer

D. low resistance in parallel with galvanometer.

Correct Answer is Option (A)

For converting galvanometer to voltmeter, a high resistance should be connected in series with galvanometer.

21. ⇒ (AIPMT 2002)

A charge q moves in a region where electric field and magnetic field both exist, then force on it is

A. $q (\vec{v} \times \vec{B})$

B. $q \vec{E} + q (\vec{v} \times \vec{B})$

C. $q \vec{E} + \vec{q} (\vec{B} \times \vec{v})$

D. $q \vec{B} + \vec{q} (\vec{E} \times \vec{v})$

Correct Answer is Option (B)

Lorentz forece

$\vec{F_{L}} = \vec{F_{e}} + \vec{F_{m}}$

= $q \vec{E} + q (\vec{v} \times \vec{B})$

22. ⇒ (AIPMT 2001)

An electron having mass m and kinetic energy E anter in uniform magnetic field B perpendiculaly, then its frequency will be

A. $\frac{e E}{q v B}$

B. $\frac{2 π m}{e B}$

C. $\frac{e B}{2 π m}$

D. $\frac{2 m}{e B E}$

Correct Answer is Option (C)

The frequency of revolution of charged particle in a perpendicular magnetic field is

$f = \frac{1}{T} = \frac{1}{\frac{2 π r}{v}} = \frac{v}{2 π r}$

$= \frac{v}{2 π} \times \frac{e B}{m v} = \frac{e B}{2 π m}$

⇒Moving Charges And Magnetism

Topic 3: Charge In Magnetic field 2