Magnetic Force(11th And 12th > Physics ) Questions and answers for exam Preparation

Question 1.

Electrons move at right angle to a magnetic field of $1.5 \times 10^{- 2}$ Tesla with a speed of $6 \times 10^{7}$ m/s. If the specific charge of the electron is $1.7 \times 10^{11}$ C/kg, then the radius of the circular path will be?

2.9 cm
3.9 cm
2.35 cm
3 cm

Explanation:-

Answer: Option C. -> 2.35 cm
:
C

r = \frac{m v}{q B} \Rightarrow \frac{v}{(q / m) . B} = \frac{6 \times 10^{7}}{1.7 \times 10^{11} \times 1.5 \times 10^{- 2}} = 2.35 \times 10^{- 2} m = 2.35 c m

Question 2.

An electron (mass = $9 \times 10^{- 31} k g,$ charge $= 1.6 \times 10^{- 19}$ C ) whose kinetic energy is $7.2 \times 10^{- 20}$ J is moving in a circular orbit in a magnetic field of $9 \times 10^{- 5} w e b e r / m^{2}$ . The radius of the orbit is

1.25 cm
2.5 cm
12.5 cm
25.0 cm

Explanation:-

Answer: Option B. -> 2.5 cm
:
B

r = \frac{\sqrt{2 m K}}{q B} = \frac{\sqrt{2 \times 9 \times 10^{- 31} \times 7.2 \times 10^{- 20}}}{1.6 \times 10^{- 19} \times 9 \times 10^{- 5}} = 2.5 c m

Question 3.

An electron and a proton enter a magnetic field perpendicularly. Both have same kinetic energy. Which of the following is true?

Trajectory of electron is less curved
Trajectory of proton is less curved
Both trajectories are equally curved
Both move on straight line path

Explanation:-

Answer: Option B. -> Trajectory of proton is less curved
:
B
By using

r = \frac{\sqrt{2 m K}}{q B}

; For both particles

q \to

same,

B \to

same,

K \to

same
Hence

r \propto \sqrt{m} \Rightarrow \frac{r_{e}}{r_{p}} = \sqrt{\frac{m_{e}}{m_{p}}}

∵ m_{p} > m_{e}

so

r_{p} > r_{e}

Since radius of the path of proton is more, hence its trajectory is less curved.

Question 4.

A proton and an $α$ particle enter a uniform magnetic field with same velocity, then ratio of the radii of path describe by them will be?

1 : 2
1 : 1
2 : 1
None of these

Explanation:-

Answer: Option A. -> 1 : 2
:
A
By using

r = \frac{m v}{q B}

;

v \to

same,

B \to

same

\Rightarrow r \propto \frac{m}{q} \Rightarrow \frac{r_{p}}{r_{α}} = \frac{m_{p}}{m_{α}} \times \frac{q_{α}}{q_{p}} = \frac{m_{p}}{4 m_{p}} \times \frac{2 q_{p}}{q_{p}} = \frac{1}{2}

Question 5.

A proton of mass m and charge +e is moving in a circular orbit of a magnetic field with energy 1MeV. What should be the energy of $α$ -particle (mass = 4 m and charge = +2e), so that it can revolve in the path of same radius?

1 MeV
4 MeV
2 MeV
0.5 MeV

Explanation:-

Answer: Option A. -> 1 MeV
:
A
By using

r = \frac{\sqrt{2 m K}}{q B}

;

r \to

same,

B \to

same

\Rightarrow K \propto \frac{q^{2}}{m}

Hence

\frac{K_{α}}{K_{p}} = {(\frac{q_{α}}{q_{p}})}^{2} \times \frac{m_{p}}{m_{α}} = {(\frac{2 q_{p}}{q_{p}})}^{2} \times \frac{m_{p}}{4 m_{p}} = 1 \Rightarrow K_{α} = K_{p} = 1 M e V

.

Question 6.

A metallic block carrying current i is subjected to a uniform magnetic induction B as shown in the figure. The moving charges experience a force F given by ……. which results in the lowering of the potential of the face …….? Assume the speed of the carriers to be v.

$e V B^k, A B C D$
$e V B^k, A B C D$
$- e V B^k, A B C D$
$- e V B^k, E F G H$

Explanation:-

Answer: Option C. ->

- e V B^k, A B C D

:
C
As the block is of metal, the charge carriers are electrons; so for current along positive x-axis, the electrons are moving along negative x-axis, i.e.

⃗ v = - v i

and as the magnetic field is along the y-axis, i.e.

⃗ B = B^j

so

⃗ F = q (⃗ v \times ⃗ B)

for this case yield

⃗ F = (- e) [- v^i \times B^j]

i.e.,

⃗ F = e v B^k

[A s^i \times^j =^k]

As force on electrons is towards the face ABCD, the electrons will accumulate on it an hence it will acquire lower potential.

A Metallic Block Carrying Current I Is Subjected To A Unifor...

Question 7.

The magnetic field is perpendicularly into the plane of the paper and a few charged particles are projected in it. Which of the following statement is true?

A represents proton and B and electron
Both A and B represent protons but velocity of A is more than that of B
Both A and B represents protons but velocity of B is more than that of A
Both A and B represent electrons, but velocity of B is more than that of A

Explanation:-

Answer: Option C. -> Both A and B represents protons but velocity of B is more than that of A
:
C
Both particles are deflecting in same direction so they must be of same sign.(i.e., both A and B represents protons)
By using

r = \frac{m v}{q B} \Rightarrow r \propto v

From given figure radius of the path described by particle B is more than that of A.
Hence

v_{B} > v_{A}

.

Question 8.

A charge particle having charge q is accelerated through a potential difference V and then it enters a perpendicular magnetic field in which it experiences a force F. If V is increased to 5V, the particle will experience a force

$F$
$5 F$
$\frac{F}{5}$
$\sqrt{5} F$

Explanation:-

Answer: Option D. ->

\sqrt{5} F

:
D

\frac{1}{2} m v^{2} = q V \Rightarrow v = \sqrt{\frac{2 q V}{m}}

. Also

F = q v B

\Rightarrow F = q B \sqrt{\frac{2 q V}{m}}

hence

F \propto \sqrt{V}

which gives

F^{'} = \sqrt{5} F

.

Question 9.

A charged particle of charge 4 mc enters a uniform magnetic field of induction $\to B = 4 \to i + y \to j + z \to k$ tesla with a velocity $\to V = 2 \to i + 3 \to j - 6 \to k$ . If the particle continues to move undeviated, then the strength of the magnetic filed induction (B) is___ tesla.

14
2
3.5
28

Explanation:-

Answer: Option A. -> 14
:
A

\to B | | \to V \frac{4}{2} = \frac{y}{3} = \frac{z}{- 6} y = 6, z = - 12 \to B = 4^i + 6^j - 12^k, B = \sqrt{4^{2} + 6^{2} + 12^{2}} B = \sqrt{196} = 14

Question 10.

A vertical wire carrying a current in the upward direction is placed in a horizontal magnetic field directed towards north. The wire will experience a force directed towards

North
South
East
West

Explanation:-

Answer: Option D. -> West
:
D
By applying Right hand thumb rule or Fleming's left hand rule, direction of force is found towards west.