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.

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]