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]

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(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]

0%

(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]

0%

(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]

0%

(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]

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(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]

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(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

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

$∴ p = 8$

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]

0%

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]

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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]

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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]

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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]

0%

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]

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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]

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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]

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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]

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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]

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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]

0%

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]

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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]