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

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

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

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

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

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

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

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

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

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

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

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

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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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 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]