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The dipole moment of a circular loop carrying a current $I$, is $m$ and the magnetic field at the centre of the loop is $B_1$ . When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is $B_2$ . The ratio $\frac{{{B_1}}}{{{B_2}}}$ is
A straight current carrying conductor is placed in such a way that the current in the conductor flows in the direction out of the plane of the paper. The conductor is placed between two poles of two magnets, as shown. The conductor will experience a force in the direction towards
A beam of protons with speed $4 \times 10^{5}\, ms ^{-1}$ enters a uniform magnetic field of $0.3\, T$ at an angle of $60^{\circ}$ to the magnetic field. The pitch of the resulting helical path of protons is close to....$cm$
(Mass of the proton $=1.67 \times 10^{-27}\, kg$, charge of the proton $=1.69 \times 10^{-19}\,C$)
Two ions of masses $4 \,{amu}$ and $16\, amu$ have charges $+2 {e}$ and $+3 {e}$ respectively. These ions pass through the region of constant perpendicular magnetic field. The kinetic energy of both ions is same. Then :
The expression for the torque acting on a coil having area of cross-section $A$, number of turns $n$, placed in a magnetic field of strength $B$, making an angle $\theta $ with the normal to the plane of the coil, when a current $i$ is flowing in it, will be
A current loop $ABCD$ is held fixed on the plane of the paper as shown in the figure. The arcs $ BC$ (radius $= b$) and $DA $ (radius $= a$) of the loop are joined by two straight wires $AB $ and $CD$. A steady current $I$ is flowing in the loop. Angle made by $AB$ and $CD$ at the origin $O$ is $30^o $. Another straight thin wire with steady current $I_1$ flowing out of the plane of the paper is kept at the origin.
Due to the presence of the current $I_1$ at the origin
Consider a thin metallic sheet perpendicular to the plane of the paper moving with speed $'v'$ in a uniform magnetic field $B$ going into the plane of the paper (See figure). If charge densities ${\sigma _1}$ and ${\sigma _2}$ are induced on the left and right surfaces, respectively, of the sheet then (ignore fringe effects)
A current carrying loop is placed in a uniform magnetic field in four different orientations, $I$, $II$, $III$ & $IV$ arrange them in the decreasing order of potential Energy
The earth’s magnetic field at a given point is $0.5 \times {10^{ - 5}}\,Wb{\rm{ - }}{m^{ - 2}}$. This field is to be annulled by magnetic induction at the center of a circular conducting loop of radius $5.0\,cm$. The current required to be flown in the loop is nearly......$A$
A triangular loop of side $l$ carries a current $I$. It is placed in a magnetic field $B$ such that the plane of the loop is in the direction of $B$. The torque on the loop is