Embibe Experts Solutions for Chapter: Magnetic Effect of Current, Exercise 3: Exercise-3

A straight wire of length $l$ carries current $I$ is moulded in the form of semicircular loop then its magnetic moment (in SI unit) is $x\times {10}^{-1}$, where $I=2\mathrm{A}$ and $l=4\mathrm{m}$. Write the value of $x$ to the nearest integer.

The coil is placed in a vertical plane and is free to rotate about a vertical axis which coincides with its diameter. A uniform magnetic field of $2 \mathrm{T}$ in the horizontal direction exists such that initially field is parallel to plane of coil. The coil rotates through an angle of $90°$ under the influence of the magnetic field when released from rest, then what is the angular speed(in $\mathrm{rad} {\mathrm{s}}^{-1}$) acquired by the coil when it has rotated by $90°$? The M.I. of the coil is $1\mathrm{kg} {\mathrm{m}}^2$ and magnetic moment of the coil is $4$ in SI unit.

A closely wound solenoid of $2000$ turns and area of cross-section $1.6\times {10}^{-4} {\mathrm{m}}^2$, carrying a current of $4.0 \mathrm{A}$, is suspended through its centre allowing it to turn in a horizontal plane. What is the torque(in SI unit) on the solenoid if a uniform horizontal magnetic field of $7.5\times {10}^{-2} \mathrm{T}$ is set up at an angle of $30°$ with the axis of the solenoid?

A Closely-wound solenoid of $1000$ turns and area of cross-section $2\times {10}^{-4}{\mathrm{m}}^2$ carries a current of $2.0$ ampere. It is placed with its horizontal axis at $30°$ with the direction of a uniform horizontal magnetic field of $0.16\mathrm{T}$ as shown in figure. What is the value of $\tau \times {10}^2$, where $\tau$ is torque (in SI unit) experienced by the solenoid?

A square current carrying loop made of thin wire and having a mass $m=10 \mathrm{g}$ can rotate without friction with respect to the vertical axis $O{O}_1$, passing through the centre of the loop at the right angles to two opposite sides of the loop. The loop is placed in a homogeneous magnetic field with an induction $B={10}^{-1} \mathrm{T}$ directed at right angles to the plane of the drawing. A current $I=2\mathrm{A}$ is flowing in the loop. The period(in second) of small oscillations that the loop performers about its position of stable equilibrium is $T$, write the value of $10T$ to the nearest integer.

A potential difference of $600\mathrm{V}$ is applied across the plates of a parallel plate condenser. The separation between the plates is $3\mathrm{mm}$. An electron projected vertically, parallel to the plates, with a velocity of $2\times {10}^6 {\mathrm{ms}}^{-1}$ moves undeflected between the plates. Find the magnitude of the magnetic field in the region between the condenser plates.

(Neglect the edge effects). (Charge of the electron $=1.6\times {10}^{-19}\mathrm{C}$) 

A beam of protons with a velocity $4\times {10}^5 {\mathrm{ms}}^{-1}$ enters a uniform magnetic field of $0.3\mathrm{T}$ at an angle of $60°$ to the magnetic field. Find the pitch of the helix in $\mathrm{cm}$ (which is the distance travelled by a proton in the beam parallel to the magnetic field during one period of rotation).

An arc of a circular loop of radius $R$ is kept in the horizontal plane and a constant magnetic field $B$ is applied in the vertical direction as shown in the figure. If the arc carries current I then find the force (in $N$) on the arc.

Use $I=\sqrt{2}\mathrm{A}, R=1\mathrm{m}$ and $B=2.5\mathrm{T}$