Question
Define the term magnetic moment of a current loop. Write the expression for the magnetic moment when an electron revolves at a speed v around an orbit of radius ‘r’ in hydrogen atom.
✓
Answer
Magnetic moment of a current loop:The torque on current loop is $\tau=\text{MB}\sin\theta$, where $\theta$ is angle between magnetic moment and magnetic field.
$\Rightarrow\text{M}=\frac{\tau}{\text{B}\sin\theta}$
If B or 1 T, $\sin\theta=1$ or $\theta=90^\circ$ then $\text{M}=\tau$.
That is the magnetic moment of a current loop is defined as the torque acting on the loop when placed in a magnetic field of 1 T such that the loop is oriented with its area vector normal to the magnetic field.
Also, M = IA
i.e., magnetic moment of a current loop is the product of current flowing in the loop and area of loop. Its direction is perpendicular to the plane of the loop and determined by using right hand thumb rule.
Magnetic moment of revolving electron,
$\text{M}=\frac{\text{evr}}{2}$
$\Rightarrow\text{M}=\frac{\tau}{\text{B}\sin\theta}$
If B or 1 T, $\sin\theta=1$ or $\theta=90^\circ$ then $\text{M}=\tau$.
That is the magnetic moment of a current loop is defined as the torque acting on the loop when placed in a magnetic field of 1 T such that the loop is oriented with its area vector normal to the magnetic field.
Also, M = IA
i.e., magnetic moment of a current loop is the product of current flowing in the loop and area of loop. Its direction is perpendicular to the plane of the loop and determined by using right hand thumb rule.
Magnetic moment of revolving electron,
$\text{M}=\frac{\text{evr}}{2}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Consider a p-n junction diode having the characteristic $\text{i}-\text{i}_0\Big(\text{e}^{\frac{\text{eV}}{\text{kT}}}-1\Big)$ where $\text{i}_0=20\mu\text{A}.$ The diode is operated at T = 300K.
→- Find the current through the diode when a voltage of 300mV is applied across it in forward bias.
- At what voltage does the current double?
Sometimes we show an idealised magnetic field which is uniform in a given region and falls to zero abruptly. One such field is represented in figure. Using Ampere's law over the path PQRS, show that such a field is not possible.
A cylindrical vessel, whose diameter and height both are equal to 30cm, is placed on a horizontal surface and a small particle P is placed in it at a distance of 5.0cm from the centre. An eye is placed at a position such that the edge of the bottom is just visible. The particle P is in the plane of drawing. Up to what minimum height should water be poured in the vessel to make the particle P visible?
Two charged conducting spheres of radii $a$ and $b$ are connected to each other by a wire. What is the ratio of electric fields at the surfaces of the two spheres? Use the result obtained to explain why charge density on the sharp and pointed ends of a conductor is higher than on its flatter portions.
→The work function of a photoelectric material is 4.0eV.
- What is the threshold wavelength?
- Find the wavelength of light for which the stopping potential is 2.5V.
A nuclide 1 is said to be the mirror isobar of nuclide 2 if $Z_1 =N_2$ and $Z_2 =N_1.$
→- What nuclide is a mirror isobar of ${_{11}}^{23}Na?$
- Which nuclide out of the two mirror isobars have greater binding energy and why?
Lenses are constructed by a material of refractive index 1.50. The magnitude of the radii of curvature are 20cm and 30cm. Find the focal lengths of the possible lenses with the above specifications.
Monochromatic radiation of wavelength 640.2 nm $(1nm = 10^{–9} m)$ from a neon lamp irradiates photosensitive material made of caesium on tungsten. The stopping voltage is measured to be 0.54 V. The source is replaced by an iron source and its 427.2 nm line irradiates the same photo-cell. Predict the new stopping voltage.
→When a Coolidge tube is operated for some time it becomes hot. Where does the heat come from?
A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in figure. The width of each stair is a and the height is b. Find the capacitance of the assembly.
