In the xy-plane, the region $y >0$ has a uniform magnetic field $B_1 \hat{k}$ and the region $y<0$ has another uniform magnetic field $B_2 \hat{k}$. A positively charged particle is projected from the origin along the positive $y$-axis with speed $v _0=\pi m s ^{-1}$ at $t =0$, as shown in the figure. Neglect gravity in this problem. Let $t = T$ be the time when the particle crosses the $x$-axis from below for the first time. If $B_2=4 B_1$, the average speed of the particle, in $m s ^{-1}$, along the $x$-axis in the time interval $T$ is. . . . . .
IIT 2018, Advanced
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A $100\, ohm$ galvanometer gives full scale deflection at $10\, mA$. How much shunt is required to read $100\, mA$ .............. $ohm$View Solution
- 2A proton and a deutron both having the same kinetic energy, enter perpendicularly into a uniform magnetic field $B$. For motion of proton and deutron on circular path of radius ${R_p}$ and ${R_d}$ respectively, the correct statement isView Solution
- 3Current $I$ is flowing along the path $ABCDA$ consisting of four edges of a cube (figure $-a$), produces a magnetic field $B_0$ at the centre of the cube. Find the magnetic field $B$ produced at the center of the cube by a current $I$ flowing along the path of the six edges $ABCGHEA$ (figure $b$)View Solution
- 4Consider a galvanometer shunted with $5\, \Omega$ resistance and $2\, \%$ of current passes through it.View Solution
What is the resistance of the given galvanometer? (In $\Omega$)
- 5A parallel plate capacitor of area $60\, cm^2$ and separation $3\, mm$ is charged initially to $90\, \mu C$. If the medium between the plate gets slightly conducting and the plate loses the charge initially at the rate of $2.5\times10^{-8}\, C/s$, then what is the magnetic field between the plates ?View Solution
- 6A galvanometer whose resistance is $120\,\Omega $ gives full scale deflection with a current of $0.05\, A$ so that it can read a maximum current of $10\, A$. A shunt resistance is added in parallel with it. The resistance of the ammeter so formed is .............. $\Omega $View Solution
- 7Figure shows a square current carrying loop $ABCD$ of side $10\,\, cm$ and current $i = 10\,A$. The magnetic moment $\vec M$ of the loop isView Solution
- 8A straight steel wire of length $‘\ell ’$ has a magnetic moment $‘M’$. It is bent in $L-$ shape. The new magnetic moment isView Solution
- 9View SolutionAn electron is projected with uniform velocity along the axis inside a current carrying long solenoid. Then :
- 10A straight wire of length $({\pi ^2})$ $metre$ is carrying a current of $2\,A$ and the magnetic field due to it is measured at a point distant $1\, cm$ from it. If the wire is to be bent into a circle and is to carry the same current as before, the ratio of the magnetic field at its centre to that obtained in the first case would beView Solution