JEE Main Magnetic Effect of Current PYQ

1. (JEE Main 2024 (Online) 6th April Morning Shift )

An element $Δ l = Δ x \hat{i}$ 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 elements $Δ x$ of $1 cm$ length is:

JEE Main 2024 (Online) 6th April Morning Shift Physics - Magnetic Effect of Current Question 1 English

A. $10 \times 10^{- 8} T$

B. $8 \times 10^{- 8} T$

C. $4 \times 10^{- 8} T$

D. $12 \times 10^{- 8} T$

Correct answer option is (C)

$\begin{aligned} B = \frac{u_{0}}{4 π} \frac{i d l \sin θ}{r^{2}} \\ \Rightarrow B = \frac{10^{- 7} \times 10 \times 10 \times 1}{\frac{1}{4}} = 4 \times 10^{- 8} T \end{aligned}$

2. (JEE Main 2024 (Online) 30th January Morning Shift )

Two insulated circular loop A and B of radius ' $a$ ' carrying a current of ' $I$ ' in the anti clockwise direction as shown in the figure. The magnitude of the magnetic induction at the centre will be :

JEE Main 2024 (Online) 30th January Morning Shift Physics - Magnetic Effect of Current Question 19 English

A. $\frac{\sqrt{2} μ_{0} I}{a}$

B. $\frac{μ_{0} I}{\sqrt{2} a}$

C. $\frac{μ_{0} I}{2 a}$

D. $\frac{2 μ_{0} I}{a}$

Correct answer option is (B)

JEE Main 2024 (Online) 30th January Morning Shift Physics - Magnetic Effect of Current Question 19 English Explanation

$∵ B_{n e t} = \frac{\sqrt{2} μ_{0} I}{2 a}$

3. (JEE Main 2024 (Online) 4th April Evening Shift )

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 __________.

JEE Main 2024 (Online) 4th April Evening Shift Physics - Magnetic Effect of Current Question 11 English

Correct answer option is 5

At point $A$

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

At point $C$

$\begin{aligned} B_{C} = \frac{μ_{0} I}{2 π (3 r)} + \frac{μ_{0} (2 I)}{r} \\ \Rightarrow \frac{B_{A}}{B_{C}} = \frac{5}{7} \end{aligned}$

4. (JEE Main 2024 (Online) 1st February Morning Shift )

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 _________.

Correct answer is 72

JEE Main 2024 (Online) 1st February Morning Shift Physics - Magnetic Effect of Current Question 30 English Explanation

$\begin{aligned} B = 6 (\frac{μ_{0} I}{4 π r}) (\sin 30^{\circ} + \sin 30^{\circ}) \\ = 6 \frac{10^{- 7} \times 4 π \sqrt{3}}{(\frac{\sqrt{3} \times 4 π}{2 \times 6})} \\ = 72 \times 10^{- 7} T \end{aligned}$

5. (JEE Main 2024 (Online) 31st January Evening Shift )

Two circular coils $P$ and $Q$ of 100 turns each have same radius of $π cm$ . The currents in $P$ and $R$ are $1 A$ and $2 A$ respectively. $P$ and $Q$ are placed with their planes mutually perpendicular with their centers coincide. The resultant magnetic field induction at the center of the coils is $\sqrt{x} m T$ , where $x =$ __________.

[Use $μ_{0} = 4 π \times 10^{- 7} {TmA}^{- 1}$ ]

Correct answer is 20

JEE Main 2024 (Online) 31st January Evening Shift Physics - Magnetic Effect of Current Question 26 English Explanation

$\begin{aligned} B_{P} = \frac{μ_{0} {Ni}_{1}}{2 r} = \frac{μ_{0} \times 1 \times 100}{2 π} = 2 \times 10^{- 3} T \\ B_{Q} = \frac{μ_{0} {Ni}_{2}}{2 r} = \frac{μ_{0} \times 2 \times 100}{2 π} = 4 \times 10^{- 3} T \\ B_{net} = \sqrt{B_{P}^{2} + B_{Q}^{2}} \\ = \sqrt{20} mT \\ x = 20 \end{aligned}$