Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : In an uniform magnetic field, speed and energy remains the same for a moving charged particle. Reason (R) : Moving charged particle experiences magnetic force perpendicular to its direction of motion.

The magnetic field at the centre of a circular coil of radius r, due to current I flowing through it, is B. The magnetic field at a point along the axis at a distance {r \over 2} from the centre is :

A coil of n number of turns wound tightly in the form of a spiral with inner and outer radii r1 and r2 respectively. When a current of strength I is passed through the coil, the magnetic field at its centre will be :

A cyclotron is working at a frequency of 10 MHz. If the radius of its dees is 60 cm. The maximum kinetic energy of accelerated proton will be : (Take : e = 1.6 $$\times$$ 10$$-$$19 C, mp = 1.67 $$\times$$ 10$$-$$27 kg)

Two charged particles, having same kinetic energy, are allowed to pass through a uniform magnetic field perpendicular to the direction of motion. If the ratio of radii of their circular paths is $$6:5$$ and their respective masses ratio is $$9:4$$. Then, the ratio of their charges will be :

A charge particle is moving in a uniform magnetic field $$(2\hat{i}+3\hat{j})\mathrm{T}$$. If it has an acceleration of $$(\alpha \hat{i}-4\hat{j})\mathrm{m}/{\mathrm{s}}^2$$, then the value of $$\alpha$$ will be :

$${\mathrm{B}}_X$$ and $${\mathrm{B}}_{\mathrm{Y}}$$ are the magnetic fields at the centre of two coils $$\mathrm{X}$$ and $$\mathrm{Y}$$ respectively each carrying equal current. If coil $$X$$ has 200 turns and $$20\mathrm{cm}$$ radius and coil $$Y$$ has 400 turns and $$20\mathrm{cm}$$ radius, the ratio of $$B_X$$ and $$B_Y$$ is :

Two concentric circular loops of radii $$r_1=30\mathrm{cm}$$ and $$r_2=50\mathrm{cm}$$ are placed in $$\mathrm{X}-\mathrm{Y}$$ plane as shown in the figure. A current $$I=7\mathrm{A}$$ is flowing through them in the direction as shown in figure. The net magnetic moment of this system of two circular loops is approximately :

A cyclotron is used to accelerate protons. If the operating magnetic field is $$1.0\mathrm{T}$$ and the radius of the cyclotron 'dees' is $$60\mathrm{cm}$$, the kinetic energy of the accelerated protons in MeV will be : $$[\mathrm{use}{\mathrm{m}}_{\mathrm{p}}=1.6\times 10^{-27}\mathrm{kg},\mathrm{e}=1.6\times 10^{-19}\mathrm{C}$$ ]

The current sensitivity of a galvanometer can be increased by : (A) decreasing the number of turns (B) increasing the magnetic field (C) decreasing the area of the coil (D) decreasing the torsional constant of the spring Choose the most appropriate answer from the options given below :

As shown in the figure, a metallic rod of linear density $$0.45\mathrm{kg}{\mathrm{m}}^{-1}$$ is lying horizontally on a smooth inclined plane which makes an angle of $$45^{\circ }$$ with the horizontal. The minimum current flowing in the rod required to keep it stationary, when $$0.15\mathrm{T}$$ magnetic field is acting on it in the vertical upward direction, will be : {Use $$g=10\mathrm{m}/{\mathrm{s}}^2$$}

A triangular shaped wire carrying $$10\mathrm{A}$$ current is placed in a uniform magnetic field of $$0.5\mathrm{T}$$, as shown in figure. The magnetic force on segment $$\mathrm{CD}$$ is (Given $$\mathrm{BC}=\mathrm{CD}=\mathrm{BD}=5\mathrm{cm}$$.)

The magnetic field at the center of current carrying circular loop is $$B_1$$. The magnetic field at a distance of $$\sqrt{3}$$ times radius of the given circular loop from the center on its axis is $$B_2$$. The value of $$B_1/B_2$$ will be

A wire X of length $$50\mathrm{cm}$$ carrying a current of $$2\mathrm{A}$$ is placed parallel to a long wire $$\mathrm{Y}$$ of length $$5\mathrm{m}$$. The wire $$\mathrm{Y}$$ carries a current of $$3\mathrm{A}$$. The distance between two wires is $$5\mathrm{cm}$$ and currents flow in the same direction. The force acting on the wire $$\mathrm{Y}$$ is

A block of mass 40 kg slides over a surface, when a mass of 4 kg is suspended through an inextensible massless string passing over frictionless pulley as shown below. The coefficient of kinetic friction between the surface and block is 0.02. The acceleration of block is. (Given g = 10 ms$$-$$2.)

A block of mass M placed inside a box descends vertically with acceleration 'a'. The block exerts a force equal to one-fourth of its weight on the floor of the box. The value of 'a' will be

A block of mass 2 kg moving on a horizontal surface with speed of 4 ms$$-$$1 enters a rough surface ranging from x = 0.5 m to x = 1.5 m. The retarding force in this range of rough surface is related to distance by F = $$-$$kx where k = 12 Nm$$-$$1. The speed of the block as it just crosses the rough surface will be :

A system of two blocks of masses m = 2 kg and M = 8 kg is placed on a smooth table as shown in figure. The coefficient of static friction between two blocks is 0.5. The maximum horizontal force F that can be applied to the block of mass M so that the blocks move together will be :

A person is standing in an elevator. In which situation, he experiences weight loss?

In the arrangement shown in figure a1, a2, a3 and a4 are the accelerations of masses m1, m2, m3 and m4 respectively. Which of the following relation is true for this arrangement?