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

Q 1 :
A 2 A current carrying straight metal wire of resistance 1 $Ω$ , resistivity $2 \times 10^{- 6} Ω m$ , area of cross-section 10 $m m^{2}$ and mass 500 g is suspended horizontally in mid-air by applying a uniform magnetic field $\vec{B}$ . The magnitude of B is ____ $\times 10^{- 1} T$ (given, g = 10 m/s²) [2024]

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(5) $R = \frac{ρ l}{A} \Rightarrow l = \frac{R A}{ρ} = \frac{1 \times 10 \times 10^{- 6}}{2 \times 10^{- 6}} = 5 m$

$i l B = m g \Rightarrow B = \frac{m g}{i l}$

$B = \frac{(0.5) (10)}{2 \times 5} = 5 \times 10^{- 1} T$

Q 2 :
A charge of 4.0 μC is moving with a velocity of $4.0 \times 10^{6} m s^{- 1}$ along the positive y-axis under a magnetic field $\vec{B}$ of strength ( $2 \hat{k}$ ) T. The force acting on the charge is $x \hat{i}$ N. The value of $x$ is ____. [2024]

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(32) $q = 4 μ C, \vec{v} = 4 \times 10^{6} \hat{j} m / s,$ $\vec{B} = 2 \hat{k} T$

$\vec{F} = q (\vec{v} \times \vec{B}) = 4 \times 10^{- 6} (4 \times 10^{6} \hat{j} \times 2 \hat{k})$

$\vec{F} = 4 \times 10^{- 6} \times 8 \times 10^{6} \hat{i} = 32 \hat{i} N$

$x = 32$

Q 3 :
A rigid wire consists of a semicircular portion of radius R and two straight sections. The wire is partially immersed in a perpendicular magnetic field $B = B_{0} \hat{j}$ as shown in the figure. The magnetic force on the wire if it has a current i is [2024]

$- 2 i B R \hat{j}$
$2 i B R \hat{j}$
$- i B R \hat{j}$
$i B R \hat{j}$

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(1)

Note: Direction of magnetic field is in $+ \hat{k}$

Force on current carrying wire,

$\vec{F} = i \vec{ℓ} \times \vec{B}$

Here, $ℓ = 2 R$

$\Rightarrow \vec{F} = - 2 i R B \hat{j}$

Q 4 :
The magnetic field existing in a region is given by $\vec{B} = 0.2 (1 + 2 x) \hat{k} T$ . A square loop of edge 50 cm carrying 0.5 A current is placed in the x – y plane with its edges parallel to the x – y axes, as shown in the figure. The magnitude of the net magnetic force experienced by the loop is ______ mN. [2024]

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(50)

$\vec{F} = i (\vec{ℓ} \times \vec{B})$

$F_{3} and F_{4} will cancel each other.$

${\vec{F}}_{1} = - 0.5 \times \frac{50}{100} \times {0.2 (1 + 4)} \hat{i}$

$= - \frac{1}{2} \times \frac{1}{2} \times 1 \hat{i} = - \frac{1}{4} \hat{i} = - 0.25 \hat{i}$

${\vec{F}}_{2} = 0.5 \times \frac{50}{100} \times {0.2 (1 + 5)} \hat{i} = \frac{1}{2} \times \frac{1}{2} \times {1.2} \hat{i} = 0.3 \hat{i}$

${\vec{F}}_{net} = 0.05 \hat{i} (N) = 50 (mN) \hat{i}$

Q 5 :
A square loop of edge length 2 m carrying a current of 2 A is placed with its edges parallel to the x-y axis. A magnetic field is passing through the x-y plane and expressed as $\vec{B} = B_{0} (1 + 4 x) \hat{k},$ where $B_{0} = 5 T .$ . The net magnetic force experienced by the loop is ______ N. [2024]

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(160)

$B (x = 0) = B_{0}, B (x = 2) = 9 B_{0}$

Also, $\vec{F} = i \vec{ℓ} \times \vec{B}$

${\vec{F}}_{1} = i ℓ B_{0} (\hat{j} \times \hat{k}) = i ℓ B_{0} (\hat{i}) = 2 \times 2 \times 5 (\hat{i}) = 20 N (\hat{i})$

${\vec{F}}_{2} = 9 i ℓ B_{0} (- \hat{j} \times \hat{k}) = 9 i ℓ B_{0} (- \hat{i}) = 2 \times 2 \times 45 (- \hat{i}) = 180 N (- \hat{i})$

$F_{net} on AD and CB = 0$

${\vec{F}}_{net} = {\vec{F}}_{2} - {\vec{F}}_{1} = 160 N (- \hat{i})$

$\Rightarrow F_{net} = 160 N$

Q 6 :
The horizontal component of Earth's magnetic field at a place is $3.5 \times 10^{- 5} T$ . A very long straight conductor carrying a current of $\sqrt{2} A$ in the direction from South-East to North-West is placed. The force per unit length experienced by the conductor is ______ $\times 10^{- 6} N / m$ . [2024]

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(35)

$F = I ℓ B \sin θ$

$\frac{F}{ℓ} = I B \sin θ = \sqrt{2} \times 3.5 \times 10^{- 5} \times \sin 45 °$

$= \sqrt{2} \times 3.5 \times 10^{- 5} \times \frac{1}{\sqrt{2}}$

$= 3.5 \times 10^{- 5} = 35 \times 10^{- 6} N/m$

Topic Question Set

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Q 2 :
A charge of 4.0 μC is moving with a velocity of $4.0 \times 10^{6} m s^{- 1}$ along the positive y-axis under a magnetic field $\vec{B}$ of strength ( $2 \hat{k}$ ) T. The force acting on the charge is $x \hat{i}$ N. The value of $x$ is ____. [2024]

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Q 3 :
A rigid wire consists of a semicircular portion of radius R and two straight sections. The wire is partially immersed in a perpendicular magnetic field $B = B_{0} \hat{j}$ as shown in the figure. The magnetic force on the wire if it has a current i is [2024]

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Topic Question Set

Q 1 : A 2 A current carrying straight metal wire of resistance 1 Ω, resistivity 2×10-6Ωm, area of cross-section 10 mm2 and mass 500 g is suspended horizontally in mid-air by applying a uniform magnetic field B→. The magnitude of B is ____ ×10-1T (given, g = 10 m/s²) [2024]

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Q 2 : A charge of 4.0 μC is moving with a velocity of 4.0×106ms-1 along the positive y-axis under a magnetic field B→ of strength (2k^) T. The force acting on the charge is xi^ N. The value of x is ____. [2024]

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Q 3 : A rigid wire consists of a semicircular portion of radius R and two straight sections. The wire is partially immersed in a perpendicular magnetic field B=B0j^ as shown in the figure. The magnetic force on the wire if it has a current i is [2024]

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Q 5 : A square loop of edge length 2 m carrying a current of 2 A is placed with its edges parallel to the x-y axis. A magnetic field is passing through the x-y plane and expressed as B→=B0(1+4x)k^, where B0=5T.. The net magnetic force experienced by the loop is ______ N. [2024]

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Q 6 : The horizontal component of Earth's magnetic field at a place is 3.5×10-5T. A very long straight conductor carrying a current of 2A in the direction from South-East to North-West is placed. The force per unit length experienced by the conductor is ______ ×10-6N/m. [2024]

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Q 2 :
A charge of 4.0 μC is moving with a velocity of $4.0 \times 10^{6} m s^{- 1}$ along the positive y-axis under a magnetic field $\vec{B}$ of strength ( $2 \hat{k}$ ) T. The force acting on the charge is $x \hat{i}$ N. The value of $x$ is ____. [2024]

Q 3 :
A rigid wire consists of a semicircular portion of radius R and two straight sections. The wire is partially immersed in a perpendicular magnetic field $B = B_{0} \hat{j}$ as shown in the figure. The magnetic force on the wire if it has a current i is [2024]