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### Forces on charged particles in electric and magnetic field

Things you should know

(A) If a charged particle is following a circular path of radius r under the influence of perpendicular electric field for example in case of electron moving around nucleus in an atom then,

(1) the force on the charged particle is inversely proportional to the square of radius of the circular path F α 1/r2

(2) The velocity of charged particle is inversely proportional to the square of the radius of circular path v α 1/√r

(3) The square of time period of revolution the charged particle is directly proportional to the cube of radius of circular path T2α r3

(B) When a charge particle is projected perpendicular to the magnetic field,

(1) It’s path is circular in plane perpendicular to the plane of magnetic field and direction of motion of charged particle.

(2) The speed and kinetic energy of particle would remain constant

(3) The velocity of charged particle only changes its direction not its magnitude

(4) The force acting on charged particle is independent of the radius of circular path but depends on the velocity of charged particle.

(5) The time period of revolution is independent of both velocity and radius of circular path of the particle.

(C) The net magnetic force on a current loop in a uniform magnetic field is zero but torque may or may not be zero

(D) The net magnetic force on a current loop in a non-uniform magnetic field is not zero but torque may or may not be zero.

(E) The torque on the coil is maximum , when the coil is suspended in the radial magnetic field.

### IITJEE physics questions

Question 1
A glass of soft drink with ice cubes floating on it is taken to an elevator which is accelerating in downwards direction. Then portion of ice inside softdrink
(a) increases
(b) decreases
(c) remains same
(d) depends on the density of soft drink

Question 2
A shell of mass m is at rest initially. It explodes into three fragments having masses in the ratio 2:2:1. THe fragments having equal masses fly off along mutuall perpandicular directions with speed v. What will be the speed of the third fragment.
(a) v
(b)√v
(c) 2√2 v
(d) 3√2 v

Question 3
If a particle moving in a magnetic field , increases its velocity, then its radius of magnetic field energy will

(a) remain constant
(b) decrease
(c) increase
(d) either b or c

Question 4
A particle of charge q and mass m moves in a circular orbit of radius r with angular speed ω. The ratio of magnitude of its magnetic moment to that of its angular momentum depends on

(a) q and m
(b) ω , m and q
(c) ω and q
(d) ω and m

Question 5
Two coils are placed close to each other. The mutual induction of the pair of coils depends upon

(a) rates at which currents are changing in the coil
(b) relative position and orientation of two coils
(c) the material of the wires of the coil
(d) the currents in the two coils

Question 6
An eye specialist prescribed spectacles having an combination of convex lens of focal length 40 cm in contact with a concave lens of focal length 25 cm . The power of this combination in diopters is

(a) +1.5
(b) -1.5
(c) +6.67
(d) -6.67

Question 7
To observe the phenomenon of interference, we need tow sources emitting light of

(a) nearly same frequency
(b) the same frequency
(c) different wavelengths
(d) same frequency and having definite phase relationship