Source And Effects Of Magnetic Field | Physics JEE previous year questions with Solutions

Q 1 :
The electrostatic force $({\vec{F}}_{1})$ and magnetic force $({\vec{F}}_{2})$ acting on a charge $q$ moving with velocity $v$ can be written [2024]

${\vec{F}}_{1} = q \vec{B}, {\vec{F}}_{2} = q (\vec{B} \times \vec{v})$
${\vec{F}}_{1} = q \vec{E}, {\vec{F}}_{2} = q (\vec{v} \times \vec{B})$
${\vec{F}}_{1} = q \vec{v} \cdot \vec{E}, {\vec{F}}_{2} = q (\vec{B} \cdot \vec{v})$
${\vec{F}}_{1} = q \vec{E}, {\vec{F}}_{2} = q (\vec{B} \times \vec{v})$

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(2)

$The electrostatic force acting on a charge, {\vec{F}}_{1} = q \vec{E}$

$The magnetic force acting on a charge {\vec{F}}_{2} = q (\vec{v} \times \vec{B})$

Q 2 :
A proton and a deuteron $(q = + e, m = 2.0 u)$ having same kinetic energies enter a region of uniform magnetic field $\vec{B}$ , moving perpendicular to $\vec{B}$ . The ratio of the radius $r_{d}$ of deuteron path to the radius $r_{p}$ of the proton path is: [2024]

$1 : 1$
$1 : \sqrt{2}$
$\sqrt{2} : 1$
$1 : 2$

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(3)

$As radius of circular path (r) = \frac{m v}{q B}$ $\dots (i)$

$Given {(K E)}_{p} = {(K E)}_{d}$

$\frac{1}{2} m_{p} v_{p}^{2} = \frac{1}{2} m_{d} v_{d}^{2} \Rightarrow m_{p} v_{p}^{2} = m_{d} v_{d}^{2}$

$As m_{d} = 2 m_{p} \Rightarrow m_{p} v_{p}^{2} = 2 m_{p} v_{d}^{2} \Rightarrow v_{p} = \sqrt{2} v_{d}$

Now from equation (i),

$\Rightarrow \frac{r_{p}}{r_{d}} = \frac{m_{p} v_{p}}{e B} \times \frac{e B}{2 m_{p} v_{d}} = \frac{1}{\sqrt{2}} = r_{d} : r_{p} = \sqrt{2} : 1$

Q 3 :
A proton moving with a constant velocity passes through a region of space without any change in its velocity. If $\bar{E}$ and $\bar{B}$ represent the electric and magnetic fields respectively, then the region of space may have:

(A) E = 0, B = 0 (B) E = 0, B ≠ 0

(C) E ≠ 0, B = 0 (D) E ≠ 0, B ≠ 0

Choose the most appropriate answer from the options given below: [2024]

(A), (B) and (C) only
(A), (C) and (D) only
(A), (B) and (D) only
(B), (C) and (D) only

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(3)

Net force on particle must be zero i.e.

$q \vec{E} + q \vec{V} \times \vec{B} = 0$

Possible cases are

(i) $\vec{E} and \vec{B} = 0$

(ii) $\vec{V} \times \vec{B} = 0, \vec{E} = 0$

(iii) $q \vec{E} = - q \vec{V} \times \vec{B}$

$\vec{E} \neq 0 and \vec{B} \neq 0$

Q 4 :
Two particles X and Y having equal charges are being accelerated through the same potential difference. Thereafter they enter normally in a region of uniform magnetic field and describes circular paths of radii $R_{1}$ and $R_{2}$ respectively. The mass ratio of X and Y is [2024]

$(\frac{R_{1}}{R_{2}})$
${(\frac{R_{2}}{R_{1}})}^{2}$
$(\frac{R_{2}}{R_{1}})$
${(\frac{R_{1}}{R_{2}})}^{2}$

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(4)

$R = \frac{m v}{q B} = \frac{p}{q B} = \frac{\sqrt{2 m (KE)}}{q B} = \frac{\sqrt{2 m q V}}{q B}$

$R \propto \sqrt{m} \Rightarrow m \propto R^{2}$

$\frac{m_{1}}{m_{2}} = {(\frac{R_{1}}{R_{2}})}^{2}$

Q 5 :
An electron with kinetic energy 5 eV enters a region of uniform magnetic field of 3 μT perpendicular to its direction. An electric field E is applied perpendicular to the direction of velocity and magnetic field. The value of E, so that the electron moves along the same path, is ____ $N C^{- 1}$ . (Given, mass of electron $= 9 \times 10^{- 31}$ kg, electric charge $= 1.6 \times 10^{- 19}$ C) [2024]

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(4) For the given condition of moving undeflected, net force should be zero.

$q E = q V B \Rightarrow E = V B$

$E = \sqrt{\frac{2 \times K E}{m}} \times B = \sqrt{\frac{2 \times 5 \times 1.6 \times 10^{- 19}}{9 \times 10^{- 31}}} \times 3 \times 10^{- 6} = 4 N / C$

Q 6 :
An electron moves through a uniform magnetic field $\vec{B} = B_{0} \hat{i} + 2 B_{0} \hat{J} T$ . At a particular instant of time, the velocity of electron is $\vec{u} = 3 \hat{i} + 5 \hat{j}$ m/s. If the magnetic force acting on electron is $\vec{F} = 5 e \hat{k}$ $N$ , where e is the charge of electron, then the value of $B_{0}$ is ____ T. [2024]

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

$5 e \hat{k} = e (3 \hat{i} + 5 \hat{j}) \times (B_{0} \hat{i} + 2 B_{0} \hat{j})$

$5 e \hat{k} = e (6 B_{0} \hat{k} - 5 B_{0} \hat{k}) \Rightarrow B_{0} = 5 T$

Q 7 :
An electron is projected with uniform velocity along the axis inside a current-carrying long solenoid. Then [2024]

the electron will continue to move with uniform velocity along the axis of the solenoid
the electron will be accelerated along the axis
the electron path will be circular about the axis
the electron will experience a force at 45° to the axis and execute a helical path

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(1)

The force on a charged particle moving in a magnetic field, $\vec{F} = q (\vec{v} \times \vec{B})$

Since $\vec{v} ∥ \vec{B}$ so the force on the electron due to the magnetic field is zero.

So it will move along the axis with uniform velocity.

Q 8 :
Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : An electron in a certain region of uniform magnetic field is moving with constant velocity in a straight line path.

Reason (R) : The magnetic field in that region is along the direction of velocity of the electron.

In the light of the above statements, choose the correct answer from the options given below: [2025]

(A) is false but (R) is true
Both (A) and (R) are true and (R) is the correct explanation of (A)
Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
(A) is true but (R) is false

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(2)

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

$\vec{F} = 0 when \vec{v} ∥ \vec{B}$

In this case, $θ = 0 ° or 180 °$

Q 9 :
Consider a long thin conducting wire carrying a uniform current $I$ . A particle having mass "M" and charge "q' is released at a distance "a" from the wire with a speed $v_{0}$ along the direction of current in the wire. The particle gets attracted to the wire due to magnetic force. The particle turns round when it is at distance x from the wire. The value of x is [ $μ_{0}$ is vacuum permeability] [2025]

$a [1 - \frac{m v_{0}}{2 q μ_{0} I}]$
$\frac{a}{2}$
$a [1 - \frac{m v_{α}}{q μ_{0} I}]$
$a e^{\frac{- 4 π m v_{0}}{q μ_{0} I}}$

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(4)

Figure

Let the velocity of the particle make an angle $θ$ with initial direction when it is at a distance x.

$\Rightarrow \frac{d x}{d t} = - v_{0} \sin θ$ ... (i)

Also, $\frac{d θ}{d t} = \frac{q}{m} (\frac{μ_{0} I}{2 π x})$ ... (ii)

$\Rightarrow \frac{d x}{d θ} = \frac{- 2 π m v_{0} x \sin θ}{q μ_{0} I}$ ... dividing eq (i) with eq (ii)

or $\int_{a}^{x} \frac{d x}{x} = \frac{- 2 π m v_{0}}{q μ_{0} I} \int_{0}^{π} \sin θ d θ$

$\ln \frac{x}{a} = \frac{- 4 π m v_{0}}{q μ_{0} I}$

Or $x = a e^{- \frac{4 π m v_{0}}{μ_{0} I q}}$

Q 10 :
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : If oxygen ion ( $O^{- 2}$ ) and Hydrogen ion ( $H^{+}$ ) enter normal to the magnetic field with equal momentum, then the path of $O^{- 2}$ ion has a smaller curvature than that of $H^{+}$ .

Reason R : A proton with same linear momentum as an electron will from a path of smaller radius of curvature on entering a uniform magnetic field perpendicularly.

In the light of the above statement, choose the correct answer from the options given below: [2025]

A is true but R is false
Both A and R true but R is NOT the correct explanation of A
A is false but R is true
Both A and R true and R is the correct explanation of A

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Radius in magnetic field, $R = \frac{m v}{q B}$

(A) mv, B are same for $O^{- 2}$ and $H^{+}$ therefore therefore (A) is correct

(B) $R = \frac{m v}{q B}$ ; mv, q, B are same, therefore (R) is incorrect.

Topic Question Set

Q 1 :
The electrostatic force $({\vec{F}}_{1})$ and magnetic force $({\vec{F}}_{2})$ acting on a charge $q$ moving with velocity $v$ can be written [2024]

Q 2 :
A proton and a deuteron $(q = + e, m = 2.0 u)$ having same kinetic energies enter a region of uniform magnetic field $\vec{B}$ , moving perpendicular to $\vec{B}$ . The ratio of the radius $r_{d}$ of deuteron path to the radius $r_{p}$ of the proton path is: [2024]

Q 4 :
Two particles X and Y having equal charges are being accelerated through the same potential difference. Thereafter they enter normally in a region of uniform magnetic field and describes circular paths of radii $R_{1}$ and $R_{2}$ respectively. The mass ratio of X and Y is [2024]

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Q 7 :
An electron is projected with uniform velocity along the axis inside a current-carrying long solenoid. Then [2024]

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Topic Question Set

Q 1 : The electrostatic force (F→1) and magnetic force (F→2) acting on a charge q moving with velocity v can be written [2024]

Q 2 : A proton and a deuteron (q=+e,m=2.0u) having same kinetic energies enter a region of uniform magnetic field B→ , moving perpendicular to B→. The ratio of the radius rd of deuteron path to the radius rp of the proton path is: [2024]

Q 4 : Two particles X and Y having equal charges are being accelerated through the same potential difference. Thereafter they enter normally in a region of uniform magnetic field and describes circular paths of radii R1 and R2 respectively. The mass ratio of X and Y is [2024]

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Q 6 : An electron moves through a uniform magnetic field B→=B0i^+2B0J^T. At a particular instant of time, the velocity of electron is u→=3i^+5j^ m/s. If the magnetic force acting on electron is F→=5ek^ N, where e is the charge of electron, then the value of B0 is ____ T. [2024]

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Q 7 : An electron is projected with uniform velocity along the axis inside a current-carrying long solenoid. Then [2024]

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Q 1 :
The electrostatic force $({\vec{F}}_{1})$ and magnetic force $({\vec{F}}_{2})$ acting on a charge $q$ moving with velocity $v$ can be written [2024]

Q 2 :
A proton and a deuteron $(q = + e, m = 2.0 u)$ having same kinetic energies enter a region of uniform magnetic field $\vec{B}$ , moving perpendicular to $\vec{B}$ . The ratio of the radius $r_{d}$ of deuteron path to the radius $r_{p}$ of the proton path is: [2024]

Q 4 :
Two particles X and Y having equal charges are being accelerated through the same potential difference. Thereafter they enter normally in a region of uniform magnetic field and describes circular paths of radii $R_{1}$ and $R_{2}$ respectively. The mass ratio of X and Y is [2024]

Q 7 :
An electron is projected with uniform velocity along the axis inside a current-carrying long solenoid. Then [2024]