Moving Charges ...

An electron moving with a speed $$u$$ along the positive $$x-$$axis at $$y=0$$ enters a region of uniform magnetic field which exists to the right of $$y-$$axis. The electron exits from the region after some time with the speed $$v$$ at coordinate $$y,$$  then :

A charge particle of charge $$q$$ is moving with speed $$v$$ in a circle of radius $$R$$ as shown in figure. Then the magnetic field at a point on axis of circle at a distance $$x$$ from centre is :

A charged particle moves inside a pipe, which is bent as shown in the figure. If $$R < \dfrac {mv}{qB}$$, then the force exerted by the pipe on charged particle at $$P$$ is (Neglect gravity) :

A particle of charge per unit mass $$\alpha$$ is released from origin with velocity $$\vec v=v_0\hat i$$ in a magnetic field $$\vec B=-B_0\hat k$$ for $$x\leq \dfrac {\sqrt 3}{2}\dfrac {v_0}{B_0\alpha}$$ and $$\vec B=0$$ for $$x > \dfrac {\sqrt 3}{2}\dfrac {v_0}{B_0\alpha}$$. The x-coordinate of the particle at time $$t\left ( > \dfrac {\pi}{3B_0\alpha}\right )$$ would be

A charged particle of specific charge (charge/mass) $$\alpha$$ is released from origin at time $$t=0$$ with velocity $$\vec v=v_0(\hat i+\hat j)$$ in a uniform magnetic field $$\vec B=B_0\hat i$$. Coordinates of the particle at time $$t=\dfrac{\pi}{B_0\alpha}$$ are

Find the circulation of the vector $$\vec{B}$$ around the square path $$T$$ with side $$l$$ located as shown in the figure above.

A horizontal wire 0.1 m long carries a current of 5 A. Find the magnitude of the magnetic field, which can support the weight of the wire. Assume wire to be of mass $$3 \times 10^{-3}kg  m^{-1}$$ :

Two very long straight parallel wires carry steady currents $$i$$ and $$2i$$ in opposite directions. The distance between the wires is $$d$$. at a certain instant of time, a point charge $$q$$ is at a point equidistant from the two wires in the plane of the wires. Its instantaneous velocity $$\vec { v } $$ is perpendicular to this plane. The magnitude of the force due to the magnetic field acting on the charge at this instant is:

Find the magnetic field $$\vec B$$.

Find the magnitude of the force $$F_2$$