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All questions of Electrostatics Potential and Capacitance for NEET Exam

A bullet of mass 2 g is having a charge of 2μC.Through what potential difference must it beaccelerated, starting from rest, to acquire a speedof 10 m/s?          [2004]
  • a)
    50 V
  • b)
    5 kV
  • c)
    50 KV
  • d)
    5 V
Correct answer is option 'C'. Can you explain this answer?

Anu Sharma answered
×10^-6 C. It is fired horizontally with a velocity of 400 m/s. If the bullet enters a uniform magnetic field of 0.5 T, find the radius of the circular path traced by the bullet.

Solution:

Given:
Mass of the bullet, m = 2 g = 2×10^-3 kg
Charge on the bullet, q = 2×10^-6 C
Velocity of the bullet, v = 400 m/s
Magnetic field, B = 0.5 T

Formula:
The equation of the motion of a charged particle in a magnetic field is given by:
F = qvBsinθ, where F is the magnetic force acting on the particle, v is the velocity of the particle, B is the magnetic field, q is the charge on the particle, and θ is the angle between v and B.

The magnetic force acts perpendicular to the velocity of the charged particle, causing it to move in a circular path with a radius given by:
r = mv/|q|B

Substituting the given values, we get:
r = (2×10^-3×400)/|2×10^-6|×0.5
r = 4 m

Therefore, the radius of the circular path traced by the bullet is 4 meters.

If the potential of a capacitor having capacity 6μF is increased from 10 V to 20 V, then increasein its energy will be [1995]
  • a)
    4x10-4 J
  • b)
    4x10-6 J
  • c)
    9x10-4 J
  • d)
    12x10-6 J
Correct answer is option 'C'. Can you explain this answer?

Capacitance of capacitor (C) = 6μF = 6 ×10–6 F; Initial potential (V1) = 10 V and final potential (V2) = 20 V.
The increase in energy (ΔU)
= (3x10-6 )x300 = 9x10-4 J .

What is the effective capacitance betweenpoints X and Y?
  • a)
    24 μF
  • b)
    18 μF
  • c)
    12 μF
  • d)
    6 μF
Correct answer is option 'D'. Can you explain this answer?

Anand Jain answered
Equivalent circuit
Here, 
Hence, no charge will flow through 20μF
C1 and C2 are in series, also C3 and C4 are in
series.
Hence, C' = 3 μF, C'' = 3 μF
C' and C'' are in parallel.
Hence net capacitance = C' + C'' = 3 + 3
= 6 μF

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