1. ⇒ (MHT CET 2021 21th September Evening Shift )

The magnetic flux near the axis and inside the air core solenoid of length $60 cm$ carrying current ' $I$ ' is $1.57 \times 10^{- 6} Wb$ . Its magnetic moment will be $[μ_{0} = 4 π \times 10^{- 7}$ , SI unit and crosssectional area is very small as compared to length of solenoid.]

A. $1 {Am}^{2}$

B. $0.25 {Am}^{2}$

C. $0.5 {Am}^{2}$

D. $0.75 {Am}^{2}$

Correct Option is (D)

Magnetic field inside the solenoid is given by

$\begin{aligned} B = \frac{μ_{0} NI}{L} \\ ∴ \frac{ϕ}{A} = \frac{μ_{0} NI}{L} \\ ∴ Magnetic moment, NIA & = \frac{ϕ L}{μ_{0}} \\ = \frac{1.5 \times 10^{- 6} \times 0.6}{4 \times 3.14 \times 10^{- 7}} \\ = 0.75 {Am}^{2} \end{aligned}$

3. ⇒ (MHT CET 2021 21th September Morning Shift )

A long solenoid carrying a current produces a magnetic field B along its axis. If the number of turns per $cm$ is doubled and the current is made ${(\frac{1}{3})}^{rd}$ then the new value of the magnetic field will be

A. $\frac{B}{3}$

B. 3B

C. $2 B$

D. $\frac{2 B}{3}$

Correct Option is (D)

Magnetic field inside a solenoid is given by

$B = μ_{0} nI$

If $n$ is doubled and $I$ is made ${(\frac{1}{3})}^{rd}$ , the value of $B$ will become $\frac{2}{3} B$ .

3. ⇒ (MHT CET 2021 20th September Evening Shift )

Two wires carrying currents $5 A$ and $2 A$ are enclosed in a circular loop as shown in the figure. Another wire carrying a current of $3 A$ is situated outside the loop. The value of $\oint \vec{B} \vec{d l}$ around the loop is ( $μ_{0} =$ permeability of free space, $\vec{d l}$ is the length of the element on the Amperion loop)

MHT CET 2021 20th September Evening Shift Physics - Moving Charges and Magnetism Question 29 English

A. $4 μ_{0}$

B. $2 μ_{0}$

C. $3 μ_{0}$

D. $μ_{0}$

Correct Option is (C)

Current of $5 A$ and $2 A$ are enclosed in the loop.

The currents are in opposite direction.

The net current enclosed by the loop is $3 A$ .

According to Ampere law,

$\oint \vec{B} d \vec{i} = μ_{0} I = 3 μ_{0}$

⇒Magnetic Field due to Electric Current