Torque Experienced by a Current Loop in a Uniform Magnetic Field

Write the expression for the force $\overrightarrow{F}$ acting on a particle of mass m and charge $q$ moving with velocity $\overrightarrow{v}$ in a magnetic field $\overrightarrow{B}$. Under what conditions will it move in a helical path?

Write the expression for the force $\overrightarrow{F}$ acting on a particle of mass m and charge $q$ moving with velocity $\overrightarrow{v}$ in a magnetic field $\overrightarrow{B}$. Under what conditions will it move in a circular path?

Write an expression for force $\overrightarrow{F}$ acting on a charge $q$ moving with a velocity $\overrightarrow{v}$ in the region, where magnetic induction $\overrightarrow{B}$ is uniform. How does the speed change, as the charge moves? Under what circumstances the force $\overrightarrow{F}$ shall be zero?

A length $L$ of a wire carries a current $I$. Show that if the wire is formed into a circular coil, the maximum torque in a given magnetic field is developed when the coil has one turn only and the maximum torque has the value,$\tau =L^{2}IB/4\pi$. 

A coil in the shape of an equilateral triangle of side $0.02 \mathrm{m}$ is suspended from a vertex such that it is hanging in a vertical plane between the pole pieces of permanent magnet producing a horizontal magnetic field $5\times {10}^{-2}$ tesla. Find the couple acting on the coil when a current of $0.1 A$ is passed through it and the magnetic field is parallel to its plane.

A given rectangular coil $OLMN$ of area $A$, carrying a given current $I$, is placed in a uniform magnetic field $\overrightarrow{B}=B\hat{k}$, in two different orientations (a) and (b) as
shown. What is the magnitude of torque experienced by this coil in the two cases ?

Why is the magnetic field radial in a moving coil galvanometer? Explain how it is achieved.

(c) A loop of irregular shape carrying current is located in an external magnetic field. If the wire is flexible, why does it change to a circular shape ?

(b) A current carrying circular loop is located in a uniform external magnetic field. If the loop is free to turn, what is its orientation of stable equilibrium ? Show that in this orientation the flux of the total field (external field $+$ field produced by the loop) is maximum. 

(a) A current carrying circular loop lies on a smooth horizontal plane. Can a uniform magnetic field be set up in such a manner that the loop turns around itself (i.e., turns about the vertical axis) ?

Write the expression for the magnetic moment $\left(\overrightarrow{m}\right)$ due to a planar square loop of side $\text{'}l\text{'}$ carrying a steady current $I$ in a vector form. As shown in Figure, this
loop is placed in a horizontal plane near a long straight conductor carrying a steady current $I_1$ at a distance $l$. Give reasons to explain that the loop will experience a net force but no torque. Write the expression for this force acting on the loop.

Why the earth's magnetic field does not affect the working of a moving coil galvanometer ?

Why is the coil wrapped on a conducting frame in a galvanometer ?

A neutron, an electron and an alpha particle moving with equal velocities, enter a uniform magnetic field going into the plane of the paper as shown in Figure (a). Trace their paths in the field and justify your answer.

What is a dead beat galvanometer ?

A moving coil galvanometer of resistance $10 \mathrm{\Omega }$ produces full scale deflection, when a current of $25 mA$ is passed through it. Describe showing full calculations, how will you convert the galvanometer into (i) a voltmeter reading up to $120 V$ and (ii) an ammeter reading up to $20 A$.

How will you convert $1 \mathrm{mA}$ full scale deflection galvanometer of resistance $100$ ohms into an ammeter to read $1 A$ (full scale deflection) and into a voltmeter to read $1$ volt (full scale deflection).

A galvanometer has a resistance of $50 \mathrm{\Omega }$. A resistance of $5 \mathrm{\Omega }$ is connected across its terminals. What part of the total current will flow through the galvanometer?

A galvanometer has a resistance of $96 \Omega$ and it is desired to pass $4\%$ of the total current through it. Calculate the value of shunt resistance.

Compare the current sensitivity and voltage sensitivity of the following moving coil galvanometers: $M_1$ and $M_2$:

$N_1=30, A_1=1.5\times {10}^{-3} {\mathrm{m}}^2$,

$B_1=0.25 T, {\mathrm{R}}_1=20 \mathrm{\Omega }$,

$N_2=35, A_2=2.0\times {10}^{-3} {\mathrm{m}}^2$,

$B_2=0.25 \mathrm{T}, {\mathrm{R}}_2=30 \mathrm{\Omega }$.

You are given that the springs in the two meters have the same torsional constants.