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

Q 1 :

An element $∆ l = ∆ x \hat{i}$ is placed at the origin and carries a large current $I$ = 10 A. The magnetic field on the y-axis at a distance of 0.5 m from the element $∆ x$ of 1 cm length is ______. [2024]

$8 \times 10^{- 8} T$
$10 \times 10^{- 8} T$
$4 \times 10^{- 8} T$
$12 \times 10^{- 8} T$

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(3)

By Biot-Savart law, $\vec{d B} = \frac{μ_{0} i}{4 π} \frac{(\vec{d l} \times \vec{r})}{r^{3}} (Tesla)$

Since element is very small,

Given: $\vec{d l} = \frac{1}{100} \hat{i} m, \vec{r} = \frac{1}{2} \hat{j} m, i = 10 A, θ = 90 °$

$= 10^{- 7} \times 10 \times \frac{(\frac{1}{100} \hat{i} \times \frac{1}{2} \hat{j})}{{(\frac{1}{2})}^{3}}$

$= 10^{- 7} \times 10 \times \frac{8}{200} \hat{k} = 4 \times 10^{- 8} T (+ \hat{k})$

Q 2 :

Two parallel long current-carrying wire separated by a distance $2 r$ are shown in the figure. The ratio of magnetic field at A to the magnetic field produced at C is $\frac{x}{7}$ . The value of $x$ is ______. [2024]

(5)

$B_{A} = \frac{μ_{0} I}{2 π r} + \frac{μ_{0} (2 I)}{2 π (3 r)} = \frac{5 μ_{0} I}{6 π r}$

$B_{C} = \frac{μ_{0} (2 I)}{2 π r} + \frac{μ_{0} I}{2 π (3 r)} = \frac{7 μ_{0} I}{6 π r}$

$∴$ $\frac{B_{A}}{B_{C}} = \frac{5}{7} \Rightarrow x = 5$

Q 3 :

Two long, straight wires carry equal currents in opposite directions as shown in the figure. The separation between the wires is 5.0 cm. The magnitude of the magnetic field at a point P midway between the wires is ______ $μT$ .

$(Given: μ_{0} = 4 π \times 10^{- 7} {TmA}^{- 1})$ [2024]

(160)

$B = (\frac{μ_{0} i}{2 π a}) \times 2 = \frac{4 π \times 10^{- 7} \times 10}{π \times (\frac{5}{2} \times 10^{- 2})}$

$= 16 \times 10^{- 5} = 160 μ T$

Q 4 :

The current of 5A flows in a square loop of sides 1m is placed in air. The magnetic field at the centre of the loop is $X \sqrt{2} \times 10^{- 7} T$ . The value of X is ______. [2024]

(40)

i = 5A,

Square of side = 1m

Magnetic field at centre will be into the plane (X), due to all four wires

${\vec{B}}_{net} = 4 B_{1}$

$B_{1} = Magnetic field due to one side,$

$B_{1} = \frac{μ_{0} . i}{4 π r} (\sin θ_{1} + \sin θ_{2}), Here θ_{1} = θ_{2} = 45 °$

$r = \frac{1}{2} m$

$B_{1} = \frac{μ_{0} . (5)}{4 π (1 / 2)} (\frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}})$

$B_{net} = 4 B_{1} = 40 \sqrt{2} \times 10^{- 2} tesla$

$∴$ $x = 40$

Q 5 :

A regular polygon of 6 sides is formed by bending a wire of length $4 π$ meter. If an electric current of $4 π \sqrt{3}$ A is flowing through the sides of the polygon, the magnetic field at the centre of the polygon would be $x \times 10^{- 7} T$ . The value of $x$ is ______. [2024]

(72)

$B = 6 (\frac{μ_{0} I}{4 π r}) (\sin 30 ° + \sin 30 °)$

$= 6 \frac{10^{- 7} \times 4 π \sqrt{3}}{(\frac{\sqrt{3} \times 4 π}{2 \times 6})} = 72 \times 10^{- 7} T \Rightarrow x = 72$

Q 6 :

Figure shows a current carrying square loop ABCD of edge length is 'a' lying in a plane. If the resistance of the ABC part is r and that of ADC part is 2r, then the magnitude of the resultant magnetic field at centre of the square loop is [2025]

$\frac{3 π μ_{0} I}{\sqrt{2} a}$
$\frac{μ_{0} I}{2 π a}$
$\frac{\sqrt{2} μ_{0} I}{3 π a}$
$\frac{2 μ_{0} I}{3 π a}$

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(3)

$\vec{B} = {\vec{B}}_{A B} + {\vec{B}}_{B C} + {\vec{B}}_{C D} + {\vec{B}}_{D A}$

${\vec{B}}_{A B} = {\vec{B}}_{B C}$

$= \frac{μ_{0} (2 I / 3)}{4 π (a / 2)} [\sin 45 ° + \sin 45 °] (- \hat{k})$

$= \frac{μ_{0} I \sqrt{2}}{3 π a} (- \hat{k})$

${\vec{B}}_{C D} = {\vec{B}}_{D A}$

$= \frac{μ_{0} (I / 3)}{4 π (a / 2)} [\sin 45 ° + \sin 45 °] (\hat{k})$

$= \frac{μ_{0} I \sqrt{2}}{6 π a} (\hat{k})$

$\vec{B} = 2 [\frac{μ_{0} I \sqrt{2}}{3 π a} (- \hat{k}) + \frac{μ_{0} I \sqrt{2}}{6 π a} (\hat{k})]$

$\Rightarrow \vec{B} = \frac{\sqrt{2} μ_{0} I}{3 π a} (- \hat{k})$

Q 7 :

Two long parallel wires X and Y, separated by a distance of 6 cm, carry currents of 5 A and 4 A, respectively, in opposite directions as shown in the figure. Magnitude of the resultant magnetic field at point P at a distance of 4 cm from wire Y is $x \times 10^{- 5} T$ . The value of x is _____. Take permeability of free space as $μ_{0} = 4 π \times 10^{- 7}$ SI units. [2025]

(1)

At P

$\vec{B} = {\vec{B}}_{1} + {\vec{B}}_{2} = \frac{μ_{0} i_{2}}{2 π r_{2}} \hat{k} - \frac{μ_{0} i_{1}}{2 π r_{1}} \hat{k}$

$\vec{B} = \frac{μ_{0}}{2 π} (\frac{4}{4} \times 10^{2} - \frac{5}{10} \times 10^{2}) \hat{k}$

$= 1 \times 10^{- 5} T$

$\Rightarrow x = 1$

Q 8 :

A current of 5 A exists in a square loop of side $\frac{1}{\sqrt{2}} m$ . Then the magnitude of the magnetic field B at the centre of the square loop will be $p \times 10^{- 6} T$ . Where, value of p is ______. [Take $μ_{0} = 4 π \times 10^{- 7} T {mA}^{- 1}$ ]. [2025]

(8)

Let B be the magnetic field due to single side then

$B = \frac{μ_{0} i}{4 π d} (\sin θ_{1} + \sin θ_{2})$

$B = \frac{10^{- 7} \times 5 \times 2}{\frac{1}{2 \sqrt{2}}} \times \frac{1}{\sqrt{2}} = 2 \times 10^{- 6}$

$∴ B_{net}$ at centre O = 4 B

$B_{net} = 8 \times 10^{- 6} T$

$∴ p = 8$

Q 9 :

A circular loop of radius $r$ is carrying current 1 A. The ratio of magnetic field at the center of the circular loop and at a distance $r$ from the center of the loop on its axis is [2023]

$1 : 3 \sqrt{2}$
$2 \sqrt{2} : 1$
$3 \sqrt{2} : 2$
$1 : \sqrt{2}$

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(2)

Magnetic field due to a current carrying circular loop on its axis is given as

$B = \frac{μ_{0} i r^{2}}{2 {(r^{2} + x^{2})}^{3 / 2}}$

$At centre, x = 0, B_{1} = \frac{μ_{0} i}{2 r}$

$At x = r, B_{2} = \frac{μ_{0} i}{2 \times 2 \sqrt{2} r}$

$\Rightarrow \frac{B_{1}}{B_{2}} = 2 \sqrt{2}$

Q 10 :

The magnitude of magnetic induction at mid-point $O$ due to current arrangement as shown in the figure will be [2023]

$\frac{μ_{0} I}{2 π a}$
$0$
$\frac{μ_{0} I}{4 π a}$
$\frac{μ_{0} I}{π a}$

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(4)

$Magnetic field due to current in B C and E T are outward at point ' O'$

$B_{0} = \frac{μ_{0} i}{4 π r} + \frac{μ_{0} i}{4 π r} = \frac{μ_{0} i}{2 π r} = \frac{μ_{0} i}{π a}$

Q 11 :

As shown in the figure, a current of 2 A flowing in an equilateral triangle of side $4 \sqrt{3}$ cm. The magnetic field at the centroid $O$ of the triangle is [2023]

(Neglect the effect of earth's magnetic field.)

$4 \sqrt{3} \times 10^{- 4} T$
$4 \sqrt{3} \times 10^{- 5} T$
$\sqrt{3} \times 10^{- 4} T$
$3 \sqrt{3} \times 10^{- 5} T$

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(4)

$d \tan 60 ° = 2 \sqrt{3}$

$d = 2 cm$

$B = 3 \times \frac{μ_{0} i}{2 π d} \sin 60 °$

$= 3 \times \frac{2 \times 10^{- 7} \times 2}{2 \times 10^{- 2}} \times \frac{\sqrt{3}}{2}$

$= 3 \sqrt{3} \times 10^{- 5}$

Q 12 :

Two long parallel wires carrying currents 8 A and 15 A in opposite directions are placed at a distance of 7 cm from each other. A point $P$ is at equidistant from both the wires such that the lines joining the point $P$ to the wires are perpendicular to each other. The magnitude of magnetic field at $P$ is ________ $\times 10^{- 6} T$ . (Given: $\sqrt{2} = 1.4$ ) [2023]

(68)

$Magnetic fields due to both wires will be perpendicular to each other.$

$B_{1} = \frac{μ_{0} i_{1}}{2 π d}, B_{2} = \frac{μ_{0} i_{2}}{2 π d}$

$B_{net} = \sqrt{B_{1}^{2} + B_{2}^{2}} = \frac{μ_{0}}{2 π d} \sqrt{i_{1}^{2} + i_{2}^{2}}$

$\Rightarrow \frac{4 π \times 10^{- 7}}{2 π \times (\frac{7}{\sqrt{2}}) \times 10^{- 2}} \times \sqrt{8^{2} + 15^{2}} (d = \frac{7}{\sqrt{2}} cm)$

$= 68 \times 10^{- 6} T$

Q 13 :

An electron in a hydrogen atom revolves around its nucleus with a speed of $6.76 \times 10^{6} {ms}^{- 1}$ in an orbit of radius $0.52 Å$ . The magnetic field produced at the nucleus of the hydrogen atom is _________ T. [2023]

(40)

$Magnetic field due to moving charge$

$B = \frac{μ_{0}}{4 π} \frac{q v \sin θ}{r^{2}}$

$B = \frac{μ_{0}}{4 π} \frac{e v \sin (π / 2)}{r^{2}}$

$B = \frac{10^{- 7} \times 1.6 \times 10^{- 19} \times 6.76 \times 10^{6}}{0.52 \times 0.52 \times 10^{- 20}}$

$\Rightarrow B = 40 T$

Q 14 :

A long cylindrical conductor with large cross section carries an electric current distributed uniformly over its cross-section. Magnetic field due to this current is :

A. maximum at either ends of the conductor and minimum at the midpoint
B. maximum at the axis of the conductor
C. minimum at the surface of the conductor
D. minimum at the axis of the conductor
E. same at all points in the cross-section of the conductor

Choose the correct answer from the options given below : [2026]

B, C Only
D Only
A, D Only
E Only

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(2)

$Solid cylinder$

$B_{\max} at surface$

$B_{\min} at axis$

Q 15 :

The current passing through a conducting loop in the form of equilateral triangle of side $4 \sqrt{3} cm$ is 2 A. The magnetic field at its centroid is $α \times 10^{- 5} T$ The value of $α$ is ______.

$(Given: μ_{0} = 4 π \times 10^{- 7} SI units)$ [2026]

$\frac{\sqrt{3}}{2}$
$\sqrt{3}$
$3 \sqrt{3}$
$2 \sqrt{3}$

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(3)

$B = \frac{μ_{0}}{4 π} \times \frac{I}{d} [\sin 60 ° + \sin 60 °] \times 3$

$B = 10^{- 7} \times \frac{2}{2 \times 10^{- 2}} (\frac{\sqrt{3}}{2} + \frac{\sqrt{3}}{2}) \times 3$

$= \sqrt{3} \times 10^{- 5} \times 3 = 3 \sqrt{3} \times 10^{- 5}$

Topic Question Set

Q 1 :

An element $∆ l = ∆ x \hat{i}$ is placed at the origin and carries a large current $I$ = 10 A. The magnetic field on the y-axis at a distance of 0.5 m from the element $∆ x$ of 1 cm length is ______. [2024]

Q 2 :

Two parallel long current-carrying wire separated by a distance $2 r$ are shown in the figure. The ratio of magnetic field at A to the magnetic field produced at C is $\frac{x}{7}$ . The value of $x$ is ______. [2024]

Q 3 :

Two long, straight wires carry equal currents in opposite directions as shown in the figure. The separation between the wires is 5.0 cm. The magnitude of the magnetic field at a point P midway between the wires is ______ $μT$ .

$(Given: μ_{0} = 4 π \times 10^{- 7} {TmA}^{- 1})$ [2024]

Q 4 :

The current of 5A flows in a square loop of sides 1m is placed in air. The magnetic field at the centre of the loop is $X \sqrt{2} \times 10^{- 7} T$ . The value of X is ______. [2024]

Q 5 :

A regular polygon of 6 sides is formed by bending a wire of length $4 π$ meter. If an electric current of $4 π \sqrt{3}$ A is flowing through the sides of the polygon, the magnetic field at the centre of the polygon would be $x \times 10^{- 7} T$ . The value of $x$ is ______. [2024]

Q 6 :

Figure shows a current carrying square loop ABCD of edge length is 'a' lying in a plane. If the resistance of the ABC part is r and that of ADC part is 2r, then the magnitude of the resultant magnetic field at centre of the square loop is [2025]

Q 8 :

A current of 5 A exists in a square loop of side $\frac{1}{\sqrt{2}} m$ . Then the magnitude of the magnetic field B at the centre of the square loop will be $p \times 10^{- 6} T$ . Where, value of p is ______. [Take $μ_{0} = 4 π \times 10^{- 7} T {mA}^{- 1}$ ]. [2025]

Q 9 :

A circular loop of radius $r$ is carrying current 1 A. The ratio of magnetic field at the center of the circular loop and at a distance $r$ from the center of the loop on its axis is [2023]

Q 10 :

The magnitude of magnetic induction at mid-point $O$ due to current arrangement as shown in the figure will be [2023]

Q 11 :

As shown in the figure, a current of 2 A flowing in an equilateral triangle of side $4 \sqrt{3}$ cm. The magnetic field at the centroid $O$ of the triangle is [2023]

(Neglect the effect of earth's magnetic field.)

Q 13 :

An electron in a hydrogen atom revolves around its nucleus with a speed of $6.76 \times 10^{6} {ms}^{- 1}$ in an orbit of radius $0.52 Å$ . The magnetic field produced at the nucleus of the hydrogen atom is _________ T. [2023]

Q 15 :

The current passing through a conducting loop in the form of equilateral triangle of side $4 \sqrt{3} cm$ is 2 A. The magnetic field at its centroid is $α \times 10^{- 5} T$ The value of $α$ is ______.

$(Given: μ_{0} = 4 π \times 10^{- 7} SI units)$ [2026]

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Topic Question Set

Q 1 : An element ∆l=∆xi^ is placed at the origin and carries a large current I = 10 A. The magnetic field on the y-axis at a distance of 0.5 m from the element ∆x of 1 cm length is ______. [2024]

Q 2 : Two parallel long current-carrying wire separated by a distance 2r are shown in the figure. The ratio of magnetic field at A to the magnetic field produced at C is x7. The value of x is ______. [2024]

Q 3 : Two long, straight wires carry equal currents in opposite directions as shown in the figure. The separation between the wires is 5.0 cm. The magnitude of the magnetic field at a point P midway between the wires is ______ μT. (Given: μ0=4π×10-7 TmA-1) [2024]

Q 4 : The current of 5A flows in a square loop of sides 1m is placed in air. The magnetic field at the centre of the loop is X2×10-7T. The value of X is ______. [2024]

Q 5 : A regular polygon of 6 sides is formed by bending a wire of length 4π meter. If an electric current of 4π3 A is flowing through the sides of the polygon, the magnetic field at the centre of the polygon would be x×10-7T. The value of x is ______. [2024]

Q 6 : Figure shows a current carrying square loop ABCD of edge length is 'a' lying in a plane. If the resistance of the ABC part is r and that of ADC part is 2r, then the magnitude of the resultant magnetic field at centre of the square loop is [2025]

Q 8 : A current of 5 A exists in a square loop of side 12m. Then the magnitude of the magnetic field B at the centre of the square loop will be p×10–6 T. Where, value of p is ______. [Take μ0=4π×10–7 T mA–1]. [2025]

Q 9 : A circular loop of radius r is carrying current 1 A. The ratio of magnetic field at the center of the circular loop and at a distance r from the center of the loop on its axis is [2023]

Q 10 : The magnitude of magnetic induction at mid-point O due to current arrangement as shown in the figure will be [2023]

Q 11 : As shown in the figure, a current of 2 A flowing in an equilateral triangle of side 43 cm. The magnetic field at the centroid O of the triangle is [2023] (Neglect the effect of earth's magnetic field.)

Q 13 : An electron in a hydrogen atom revolves around its nucleus with a speed of 6.76×106 ms-1 in an orbit of radius 0.52 Å. The magnetic field produced at the nucleus of the hydrogen atom is _________ T. [2023]

Q 15 : The current passing through a conducting loop in the form of equilateral triangle of side 43 cm is 2 A. The magnetic field at its centroid is α×10-5 T The value of α is ______. (Given: μ0=4π×10-7 SI units) [2026]

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Q 1 :

An element $∆ l = ∆ x \hat{i}$ is placed at the origin and carries a large current $I$ = 10 A. The magnetic field on the y-axis at a distance of 0.5 m from the element $∆ x$ of 1 cm length is ______. [2024]

Q 2 :

Two parallel long current-carrying wire separated by a distance $2 r$ are shown in the figure. The ratio of magnetic field at A to the magnetic field produced at C is $\frac{x}{7}$ . The value of $x$ is ______. [2024]

Q 3 :

Two long, straight wires carry equal currents in opposite directions as shown in the figure. The separation between the wires is 5.0 cm. The magnitude of the magnetic field at a point P midway between the wires is ______ $μT$ .

$(Given: μ_{0} = 4 π \times 10^{- 7} {TmA}^{- 1})$ [2024]

Q 4 :

The current of 5A flows in a square loop of sides 1m is placed in air. The magnetic field at the centre of the loop is $X \sqrt{2} \times 10^{- 7} T$ . The value of X is ______. [2024]

Q 5 :

A regular polygon of 6 sides is formed by bending a wire of length $4 π$ meter. If an electric current of $4 π \sqrt{3}$ A is flowing through the sides of the polygon, the magnetic field at the centre of the polygon would be $x \times 10^{- 7} T$ . The value of $x$ is ______. [2024]

Q 6 :

Figure shows a current carrying square loop ABCD of edge length is 'a' lying in a plane. If the resistance of the ABC part is r and that of ADC part is 2r, then the magnitude of the resultant magnetic field at centre of the square loop is [2025]

Q 8 :

A current of 5 A exists in a square loop of side $\frac{1}{\sqrt{2}} m$ . Then the magnitude of the magnetic field B at the centre of the square loop will be $p \times 10^{- 6} T$ . Where, value of p is ______. [Take $μ_{0} = 4 π \times 10^{- 7} T {mA}^{- 1}$ ]. [2025]

Q 9 :

A circular loop of radius $r$ is carrying current 1 A. The ratio of magnetic field at the center of the circular loop and at a distance $r$ from the center of the loop on its axis is [2023]

Q 10 :

The magnitude of magnetic induction at mid-point $O$ due to current arrangement as shown in the figure will be [2023]

Q 11 :

As shown in the figure, a current of 2 A flowing in an equilateral triangle of side $4 \sqrt{3}$ cm. The magnetic field at the centroid $O$ of the triangle is [2023]

(Neglect the effect of earth's magnetic field.)

Q 13 :

An electron in a hydrogen atom revolves around its nucleus with a speed of $6.76 \times 10^{6} {ms}^{- 1}$ in an orbit of radius $0.52 Å$ . The magnetic field produced at the nucleus of the hydrogen atom is _________ T. [2023]

Q 15 :

The current passing through a conducting loop in the form of equilateral triangle of side $4 \sqrt{3} cm$ is 2 A. The magnetic field at its centroid is $α \times 10^{- 5} T$ The value of $α$ is ______.

$(Given: μ_{0} = 4 π \times 10^{- 7} SI units)$ [2026]