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]

(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]

(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]

(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]

(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]

(35)

$F = I ℓ B \sin θ$

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

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

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

Q 7 :

A 4.0 cm long straight wire carrying a current of 8 A is placed perpendicular to an uniform magnetic field of strength 0.15 T. The magnetic force on the wire is ______ mN. [2025]

(48)

$F = I l B$

$F = 8 \times \frac{4}{100} \times 0.15 = 48 \times 10^{- 3} N = 48 mN$

Q 8 :

A massless square loop of wire of resistance $10 Ω$ supporting a mass of 1 g hangs vertically with one of its sides in a uniform magnetic field of $10^{3} G$ , directed outwards in the shaded region. A dc voltage $V$ is applied to the loop. For what value of $V$ , the magnetic force will exactly balance the weight of the supporting mass of 1 g? [2023]

(If sides of the loop = 10 cm, $g = 10 {ms}^{- 2}$ )

$\frac{1}{10} V$
$100 V$
$1 V$
$10 V$

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(4)

$F_{m} = m g$

$∴$ $I L B = m g$

$∴$ $(\frac{v}{R}) L B = m g$

$∴$ $v = \frac{m g R}{L B} = \frac{(1 \times 10^{- 3} kg) (10 {m/s}^{2}) (10 Ω)}{(0.1 m) (10^{3} \times 10^{- 4} T)} = 10 V$

Q 9 :

Two long straight wires $P$ and $Q$ carrying equal current 10 A each were kept parallel to each other at 5 cm distance. Magnitude of magnetic force experienced by 10 cm length of wire $P$ is $F_{1}$ . If the distance between the wires is halved and the currents on them are doubled, the force $F_{2}$ on 10 cm length of wire $P$ will be [2023]

$10 F_{1}$
$8 F_{1}$
$\frac{F_{1}}{8}$
$\frac{F_{1}}{10}$

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(2)

$Force per unit length between two parallel straight wires$

$= \frac{μ_{0} i_{1} i_{2}}{2 π d}$

$\frac{F_{1}}{F_{2}} = \frac{\frac{μ_{0} {(10)}^{2}}{2 π (5)}}{\frac{μ_{0} {(20)}^{2}}{2 π (\frac{5}{2})}} = \frac{1}{8} \Rightarrow F_{2} = 8 F_{1}$

Q 10 :

A current carrying rectangular loop $P Q R S$ is made of uniform wire. The length $P R = Q S = 5$ cm and $P Q = R S = 100$ cm. If the ammeter current reading changes from $I$ to $2 I$ , the ratio of magnetic forces per unit length on the wire $P Q$ due to wire $R S$ in the two cases respectively $f_{P Q}^{I} : f_{P Q}^{2 I}$ is [2023]

1 : 2
1 : 4
1 : 5
1 : 3

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(2)

$Force between two current-carrying wires = \frac{μ_{0} I_{1} I_{2}}{2 π d} \times L$

$Here I_{1} and I_{2} are equal$

$F = \frac{μ_{0} I^{2}}{2 π d} \times L$

$F \propto I^{2}$

$\frac{F_{I}}{F_{2 I}} = \frac{I^{2}}{4 I^{2}} = \frac{1}{4}$

Q 11 :

An electron is moving along the positive $x$ -axis. If the uniform magnetic field is applied parallel to the negative $z$ -axis, then [2023]

A. The electron will experience magnetic force along positive y-axis

B. The electron will experience magnetic force along negative y-axis

C. The electron will not experience any force in magnetic field

D. The electron will continue to move along the positive x-axis

E. The electron will move along circular path in magnetic field

Choose the correct answer from the options given below:

B and E only
A and E only
C and D only
B and D only

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(1)

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

Force will be along the negative y-axis.

As magnetic force is perpendicular to velocity, the path of the electron must be a circle.

Q 12 :

A single turn current loop in the shape of a right angle triangle with sides 5 cm, 12 cm, 13 cm is carrying a current of 2 A. The loop is in a uniform magnetic field of magnitude 0.75 T whose direction is parallel to the current in the 13 cm side of the loop. The magnitude of the magnetic force $x$ on the 5 cm side will be $\frac{x}{130} N$ . The value of $x$ is _______. [2023]

(9)

$Force on 5 cm side is$

$| \vec{F} |$ $= I L B \sin θ$

$= (2) (5 \times 10^{- 2}) \times \frac{3}{4} \times \frac{12}{13} = \frac{9}{130} N$

$So, x = 9$

Q 13 :

A straight wire AB of mass 40 g and length 50 cm is suspended by a pair of flexible leads in a uniform magnetic field of magnitude 0.40 T as shown in the figure. The magnitude of the current required in the wire to remove the tension in the supporting leads is _________ A. (Take $g = 10 {ms}^{- 2}$ ) [2023]

(2)

$For equilibrium M g = I l B$

$I = \frac{m g}{ℓ B} = \frac{40 \times 10^{- 3} \times 10}{50 \times 10^{- 2} \times 0.4} = 2 A$

Q 14 :

Three long straight wires carrying current are arranged mutually parallel as shown in the figure. The force experienced by $15 cm$ length of wire Q is _____. [2026]

$6 \times 10^{- 6} N towards R$
$6 \times 10^{- 7} N towards R$
$6 \times 10^{- 7} N towards P$
$6 \times 10^{- 6} N towards P$

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(1)

$F_{net} = \frac{μ_{0}}{2 π} I_{0} (\frac{I_{1}}{d_{1}} + \frac{I_{2}}{d_{2}}) ℓ$

$F_{net} = 2 \times 10^{- 7} \times (\frac{3}{3} + \frac{2}{2}) \times \frac{15 \times 10^{- 2}}{10^{- 2}}$

$= 4 \times 15 \times 10^{- 7}$

$F_{net} = 6 \times 10^{- 6} N$

Topic Question Set

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]

Q 7 :

A 4.0 cm long straight wire carrying a current of 8 A is placed perpendicular to an uniform magnetic field of strength 0.15 T. The magnetic force on the wire is ______ mN. [2025]

Q 14 :

Three long straight wires carrying current are arranged mutually parallel as shown in the figure. The force experienced by $15 cm$ length of wire Q is _____. [2026]

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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]

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]

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]

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]

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]

Q 7 : A 4.0 cm long straight wire carrying a current of 8 A is placed perpendicular to an uniform magnetic field of strength 0.15 T. The magnetic force on the wire is ______ mN. [2025]

Q 10 : A current carrying rectangular loop PQRS is made of uniform wire. The length PR=QS=5 cm and PQ=RS=100 cm. If the ammeter current reading changes from I to 2I, the ratio of magnetic forces per unit length on the wire PQ due to wire RS in the two cases respectively fPQI:fPQ2I is [2023]

Q 14 : Three long straight wires carrying current are arranged mutually parallel as shown in the figure. The force experienced by 15 cm length of wire Q is _____. [2026]

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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]

Q 7 :

A 4.0 cm long straight wire carrying a current of 8 A is placed perpendicular to an uniform magnetic field of strength 0.15 T. The magnetic force on the wire is ______ mN. [2025]

Q 14 :

Three long straight wires carrying current are arranged mutually parallel as shown in the figure. The force experienced by $15 cm$ length of wire Q is _____. [2026]