Exercise 1

In a moving coil galvanometer, torque on the coil can be expressed as τ=ki, where is current through the wire and k is constant. The rectangular coil of the galvanometer having numbers of turns N, area A and moment of inertia I is placed in magnetic field B. Find, K in terms of given parameters N, I, A and B.

An iron ring of relative permeability ${\mu }_r$ has windings of insulated copper wire of $n$ turns per metre. When the current in the windings is $I$, find the expression for the magnetic field in the ring.

What is the radius of the path of an electron ( mass $9\times {10}^{-31} \mathrm{kg}$ and charge$1.6\times {10}^{-19} \mathrm{C}$ moving at a speed of $3\times {10}^7 {\mathrm{ms}}^{-1}$ in a magnetic field of $6\times {10}^{-4} \mathrm{T}$ perpendicular to it? What is its frequency? Calculate its energy in $\mathrm{keV}$. $\left(1 \mathrm{eV}=1.6\times {10}^{-19 }\mathrm{J}\right)$

A coil of area $A$, number of turns $\mathrm{N}$ and resistance $R$ is rotating in a radial magnetic field $B$ with an angular speed $\omega$. What is the maximum power consumed by the coil?

The deflection in galvanometer falls to ${\left(\frac{1}{4}\right)}^{th}$, when it is shunted by $3 \Omega$ . If additional shunt of $\mathrm{2 \Omega }$ is connected in parallel to earlier shunt, the deflection in galvanometer falls to ${\left(\frac{1}{\alpha }\right)}^{th}$ value. Write the value of $2\alpha$.

A closed curve encircles several conductors. The line integral$\int \overrightarrow{\mathrm{B}}.\overrightarrow{\mathrm{dl}}$  around this curve is $3.83\times {10}^{-7} \mathrm{T}-\mathrm{m}$. What is the net current in the conductors? 

A rectangular loop consists of $N$ closed wrapped turns and has dimensions $a\times b$. The loop is hinged along the Y-axis. What is the magnitude of the torque exerted on the loop by a uniform magnetic field $B=B_0$ direction shown. The torque acting on the loop is