Moving Charges ...

Two long straight parallel wires, carrying (adjustable) current $$I_1$$ and $$I_2$$, are kept at a distance d apart. If the force 'F' between the two wires is taken as 'positive' when the wires repel each other and 'negative' when the wires attract each other, the graph showing the dependence of 'F', on the product $$I_1I_2$$, would be

An electron gun is placed inside a long solenoid of radius $$R$$ on its axis. The solenoid has $$n$$ tums / length and carries a current $$I$$. The electron gun shoots an electron along the radius of the solenoid with speed $$\upsilon $$. If the electron does not hit the surface of the solenoid, maximum possible value of $$\upsilon $$ is (allsymbols have their standard meaning):

An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii $$r_e, r_p, r_{\alpha}$$ respectively in a uniform magnetic field B. The relation between $$r_e, r_p, r_{\alpha}$$ is?

A negative test charge is moving near a long straight wire carrying a current. The force acting on the test charge is parallel to the direction of the current. The motion of the charge is :

An electron traveling with a speed $$\mathrm{u}$$ along the positive $$\mathrm{x}$$-axis enters into a region of magnetic field where $$\mathrm{B}=-\mathrm{B}_{0}\hat{\mathrm{k}}(\mathrm{x}>0)$$. It comes out of the region with speed $$\mathrm{v}$$ then :

$$\mathrm{A}$$ magnetic field $$\vec{\mathrm{B}}=\mathrm{B}_{0}\hat{\mathrm{j}}$$ exists in the region a $$<\mathrm{x}<2\mathrm{a}$$ and $$\vec{\mathrm{B}}=-\mathrm{B}_{0}\hat{\mathrm{j}}$$ , in the region $$2\mathrm{a}<\mathrm{x}<3\mathrm{a}$$, where $$\mathrm{B}_{0}$$ is a positive constant. $$\mathrm{A}$$ positive point charge moving with a velocity $$\vec{\mathrm{v}}=\mathrm{v}_{0}\hat{\mathrm{i}}$$, where $$\mathrm{v}_{0}$$ is a positive constant, enters the magnetic field at $$\mathrm{x}=\mathrm{a}$$. The trajectory of the charge in this region can be like, 

A proton and alpha particle both enter a region of uniform magnetic field B, moving at right angles to the field B. If the radius of circular orbits for both the particles is equal and the kinetic energy acquired by proton is 1 MeV, the energy acquired by the alpha particle will be:

Two identical bar magnets are fixed with their centres at a distance d apart. A stationary charge Q is placed at P in between the gap of the two magnets at a distance D from the centre O as shown in the figure.
The force on the charge Q is

Current sensitivity of a moving coil galvanometer is $$5$$ div/mA and its voltage sensitivity (angular deflection per unit voltage applied) is $$20$$ div/V. The resistance of the galvanometer is?

A proton carrying $$1MeV$$ kinetic energy is moving in a circular path of radius $$R$$ in uniform magnetic field. What should be the energy of an $$\alpha$$-particle to describe a circle of same radius in the same field?