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The magnetic field existing in a region is given by $\overrightarrow{\mathrm{B}}=0.2(1+2 \mathrm{x}) \hat{\mathrm{k} T}$. A square loop of edge $50 \mathrm{~cm}$ carrying $0.5 \mathrm{~A}$ current is placed in $x-y$ plane with its edges parallel to the $x-y$ axes, as shown in figure. The magnitude of the net magnetic force experienced by the loop is___________. $\mathrm{mN}$.
A voltmeter having resistance of $50 × 10^3$ $Omega$ is used to measure the voltage in a circuit. To increase the range of measurement $3$ times the additional series resistance required is
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 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 :-
A voltmeter has resistance of $2000\, ohms$ and it can measure upto $2\,V$. If we want to increase its range to $10\, V$, then the required resistance in series will be ........... $\Omega $
Infinite number of straight wires each carrying current $I$ are equally placed as shown in the figure. Adjacent wires have current in opposite direction. Net magnetic field at point $P$ is