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A particle of mass $m = 1.67 \times 10^{-27}\, kg$ and charge $q = 1.6 \times 10^{-19} \, C$ enters a region of uniform magnetic field of strength $1$ $tesla$ along the direction shown in the figure. the radius of the circular portion of the path is :-
Two very thin metallic wires placed along $X$ and $Y$-axis carry equal currents as shown here. $AB$ and $CD$ are lines at $45^\circ $ with the axes with origin of axes at $O$. The magnetic field will be zero on the line
Two mutually perpendicular insulated conducting wires carrying equal currents $I$, intersect at origin. Then the resultant magnetic induction at point $P(2m, 3m)$ will be
A charge $q$ $coulomb$ moves in a circle at $n$ revolutions per second and the radius of the circle is $r$ $metre$. Then magnetic field at the centre of the circle is
Two long parallel wires are at a distance $R$ apart. They carry steady equal currents in the same directions as shown in the figure. The ratio of magnetic fields at $A, B$ and $C$ respectively, is
A galvanometer of $10 \,\Omega$ resistance gives full scale deflection with $0.01$ ampere of current. It is to be converted into an ammeter for measuring $10$ ampere current. The value of shunt resistance required will be
A wire in the form of a circular loop of one turn carrying a current produces a magnetic field $B$ at the centre. If the same wire is looped into a coil of two turns and carries the same current, the new value of magnetic induction at the centre is