# Conservation of Energy in Case of Electrostatics

## Trending Questions

**Q.**The closest distance of approach of an alpha particle travelling with a velocity ‘v’ towards Al13 nucleus is ‘d’. The closest distance of approach of an alpha particle travelling with velocity ‘4v’ towards Fe26 nucleus is

- d8

- d4

- d8

- 8d

**Q.**A proton, a deuteron and an α-particle is accelerated through the same potential difference from rest, enters a region of uniform magnetic field, moving at right angles to it. What is the ratio of their kinetic energies?

- 1:1:2
- 2:2:1
- 1:3:3
- 1:2:3

**Q.**A bullet of mass m and charge q is fired towards a solid uniformly charged sphere of radius R and total charge +q. If it strikes the surface of sphere with speed u, find the minimum speed u so that it can penetrate through the sphere. (Neglect all resistance forces or friction acting on bullet except electrostatic forces)

**Q.**A body of mass 1 g and carrying a charge 10−8 C passes through two points P and Q. P and Q are at electric potential 600 V and 0 V respectively. The velocity of the body at Q is 20×10−2 ms−1. Its velocity at P is √x×10−3 ms−1. The value of x is

**Q.**The magnetic field of a plane electromagnetic wave is given by:

→B=B0^i[cos(kz−ωt)]+B1^jcos(kz+ωt), Where B0=3×10−5 T and B1=2×10−6 T

The rms value of the force experienced by a stationary charge Q=10−4 C at z=0 is closest to

- 0.1 N
- 0.6 N
- 3×10−2 N
- 0.9 N

**Q.**A block of mass 1 kg containing a net positive charge 10−10 C is placed on a smooth horizontal table which terminates in a vertical wall as shown in figure. The distance of the block from the wall is 2 m. A horizontal electric field 1010 N/C towards right is switched on. Assuming elastic collision (if any), find the time period of the resulting oscillatory motion.

- 1 s
- 2 s
- 3 s
- 4 s

**Q.**The electric field intensity due to a thin infinitely long wire of uniform linear charge density λ at O as shown in the figure is

- λ2πϵ0R
- √2λ2πϵ0R
- λ√52πϵ0R
- 0

**Q.**Figure shows a charge +Q clamped at a point in free space. From a large distance another charge particle of charge −q and mass of m is thrown towards +Q with an impact parameter d as shown with speed v. How many positions for minimum separation would be attained for the particle.

- 1
- 2
- 3
- 4

**Q.**A charged particle enters a uniform magnetic field, directed perpendicular to its velocity. The magnetic field may

- increase the kinetic energy of the particle.
- decrease the kinetic energy of the particle.
- change the direction of motion of the particle.
- Both options (A) and (C)

**Q.**Energy per unit volume for a capacitor having area A and separation d kept at potential difference V is given by

- 12ϵ0V2d2
- ϵ0V2d2
- 12CV2
- Q22C

**Q.**A charged particle q is fired towards another charged particle Q which is fixed, with a speed v. It approaches Q upto a closest distance r and then returns. If q is given speed 2v, the closest distance of approach would be: [AIEEE-2004]

- r/4
- r/2
- 2r
- r

**Q.**A charge 3 μC is released from rest from a point P in an electric field where electric potential is 20 V. When the charge reaches slowly at infinity its kinetic energy becomes:

- 60 μJ
- 45 μJ
- 30 μJ
- 120 μJ

**Q.**The energy of a 100 μF capacitor charged to 6 kV is used to lift a 50 kg mass (by powering a motor by energy of capacitor) without incurring any losses. What would be the greatest vertical height through which mass could be raised?

(Take g=10 m/s2)

- 0.6 mm
- 3.6 m
- 1.6 m
- 1.2 mm

**Q.**A particle of mass 0.01 kg and charge 10−6 C is placed at rest in a uniform electric field 2×106 N/C and then released. The kinetic energy attained by the particle after moving a distance of 2 m is

[Assume gravity free space]

- 1 J
- 2 J
- 3 J
- 4 J

**Q.**An elementary particle of mass m and charge +e is projected with velocity at a much more massive particle of charge Ze, where Z > 0. What is the closest possible approach of the incident particle

- Ze28πϵ0mv2
- Ze4πϵ0mv2
- Ze22πϵ0mv2
- Ze8πϵ0mv2

**Q.**A block of mass 4 kg carrying a charge 50 μC is connected to a spring for which spring constant is 100 N/m. The block lies on a frictionless horizontal track and the system is immersed in a uniform electric field of magnitude 5×105 V/m, directed as shown in figure. If the block is released suddenly from rest when the spring is unstretched then the maximum extension in the spring is

- 20 cm
- 30 cm
- 40 cm
- 50 cm

**Q.**An automobile spring extends 0.2 m for 5000 N load. The ratio of potential energy stored in the spring to the potential energy stored in a 10μF capacitor at a potential difference of 10, 000 V will be

- 14
- 1
- 12
- 2

**Q.**A particle of mass m and charge q is released from rest in an electric field E. Then the K.E. after time t will be

- 2E2t2mq
- E2q2t22m
- Eq2m2t2
- Eqm2t

**Q.**A particle of specific charge (charge/mass) α starts moving from the origin from rest under the action of an electric field →E=E0 ^i and magnetic field →B=B0 ^k. Its velocity at (x0, y0, 0) is (4^i−3^j). The value of x0 is :

(All parameters are in SI unit.)

- 13αE02B0
- 16αB0E0
- 252αE0
- 5α2B0

**Q.**A particle of charge q and mass m moving under the influence of uniform electric field E ^i and a uniform magnetic field −B ^i moves from point P (0, a) to Q (2a, a) where O (0, 0) is origin. The velocity of the particle at Point P is v ^i and at Q is 2v ^i. The rate of work done by the electric field & magnetic field on particle at point P will be respectively:

- 34mv3a, 0
- 34mv3a , 32mv3a
- 32amv3, 0
- 0, mv32a

**Q.**Two unchanged spheres are rubbed together and then separated by a distance of 2cm in air. If the force of attraction between them is 22.5N. Then the number of electrons lost by positively charged sphere is

- 625
- 6.25×1018
- 6.25×1012
- 225

**Q.**A test charge q is made to move in the electric field of a point charge Q along two different closed paths (Figure). First path has sections along and perpendicular to lines of electric field. Second path is a rectangular loop of the same area as the first loop. How does the work done compare in the two cases?

**Q.**The potential barrier between the p−n junction is 0.8 V. If the width of the depletion region is 8×10−7 m then the intensity of electric field in this region is ____×106 V/m.

**Q.**There exists a region of electric field with potential difference of 25 V as shown in figure. An electron enters this region at speed of v = 3 ×106 m/s at angle of α and emerges out of region at angle β. The sin αsin β is [Electric field exist in given region only]

e=1.6×10−19, m=9.1×10−31

**Q.**For the situation described in the figure, the magnetic field changes with time according to, B=(2.00t3−4.00t2+0.8) T. What is the magnitude of electric field at point P1 when t=0.02 s and r1=0.02 m.

- 1 N/C
- 2.5 N/C
- 3 N/C
- 0.3 N/C

**Q.**A particle of charge −1 C and mass 0.2 g moves in a circle of radius 1 m around an infinite long line charge of linear charge density +1 nC/m. The time period of motion is

- π150 s
- π75 s
- π100 s
- π60 s

**Q.**A particle of specific charge α starts moving from the origin under the action of an electric field →E=E0 ^i and magnetic field →B=B0 ^k. Its velocity at (x0, y0, 0) is (4^i+3^j). The value of x0 is:

- 5α2B0
- 13αE02B0
- 16αE0E0
- 252αB0

**Q.**An electron with a kinetic energy of 100 eV enters the space between the plates of a parallel plate capacitor made of two dense metal grids at an angle of 30∘ with the plates of capacitor and leaves this space at an angle of 45∘ with the plates. What is the potential difference of the capacitor ?

- 100 V
- 50 V
- 150 V
- 200 V

**Q.**For the shown system of fixed charges, where should a third charge of 3 nC be placed, so that the system remains in equilibrium.

- 0.37 m from 4 nC charge toward left
- 0.47 m from 4 nC charge toward left
- 0.67 m from 4 nC charge toward left
- 0.57 m from 4 nC charge toward left

**Q.**

Two electric charges of +10−9C and −10−9C are placed at the corners A and B of an equilateral triangle ABC side 5cm.The electric intensity at C is

- 1800N/C
- 3600N/C
- 900N/C
- 2700N/C