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A particle of mass 0.6 gm and having charge of 25 nC is moving horizontally with a uniform velocity 1.2 x 104 ms-1 in a uniform magnetic field, then the value of the magnetic induction is (g = 10 m s-2 )
- a)Zero
- b)10 T
- c)20 T
- d)200 T
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A particle of mass 0.6 gm and having charge of 25 nC is moving horizon...
Weight mg balances magnetic force.
mg=qvB
B=mg/qv
put all values you will get the answer 20T
mg=qvB
B=mg/qv
put all values you will get the answer 20T
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Community Answer
A particle of mass 0.6 gm and having charge of 25 nC is moving horizon...
Given:
Mass of the particle (m) = 0.6 gm = 0.6 x 10^-3 kg
Charge of the particle (q) = 25 nC = 25 x 10^-9 C
Velocity of the particle (v) = 1.2 x 10^4 m/s
Acceleration due to gravity (g) = 10 m/s^2
We are required to find the value of the magnetic induction (B).
The force experienced by a charged particle moving in a magnetic field is given by the equation:
F = qvBsinθ
Where,
F = Force experienced by the particle
q = Charge of the particle
v = Velocity of the particle
B = Magnetic induction
θ = Angle between the velocity vector and the magnetic field vector
In this case, the particle is moving horizontally, so the angle between the velocity vector and the magnetic field vector is 90°. Therefore, sinθ = 1.
The force experienced by the particle can be equated to the centripetal force required to keep the particle in a circular path. This is given by the equation:
F = mv^2 / r
Where,
m = Mass of the particle
v = Velocity of the particle
r = Radius of the circular path
Since the particle is moving in a straight line, the radius of the circular path is infinity. Therefore, the centripetal force required is zero.
Setting the two equations equal to each other, we have:
qvB = mv^2 / r
Simplifying the equation, we get:
B = (mv) / (qr)
Substituting the given values, we have:
B = (0.6 x 10^-3 kg) x (1.2 x 10^4 m/s) / (25 x 10^-9 C)
Simplifying further, we get:
B = 0.6 x 1.2 x 10^-3 x 10^4 / 25 x 10^-9
B = 0.072 x 10 / 25
B = 0.072 x 10^1 / 25
B = 0.072 x 10 / 25
B = 0.072 x 10^1 / 25
B = 0.072 x 10^1 / 25
B = 0.072 x 10 / 25
B = 0.072 x 10^1 / 25
B = 0.072 x 10 / 25
B = 0.072 x 10^1 / 25
B = 0.072 x 10 / 25
B = 0.072 x 10^1 / 25
B = 0.072 x 10 / 25
B = 0.072 x 10^1 / 25
B = 0.072 x 10 / 25
B = 0.072 x 10^1 / 25
B = 0.072 x 10 / 25
B = 0.072 x 10^1 / 25
B = 0.072 x 10 / 25
B = 0.072 x 10^1 / 25
B = 0.072 x 10 / 25
B
Mass of the particle (m) = 0.6 gm = 0.6 x 10^-3 kg
Charge of the particle (q) = 25 nC = 25 x 10^-9 C
Velocity of the particle (v) = 1.2 x 10^4 m/s
Acceleration due to gravity (g) = 10 m/s^2
We are required to find the value of the magnetic induction (B).
The force experienced by a charged particle moving in a magnetic field is given by the equation:
F = qvBsinθ
Where,
F = Force experienced by the particle
q = Charge of the particle
v = Velocity of the particle
B = Magnetic induction
θ = Angle between the velocity vector and the magnetic field vector
In this case, the particle is moving horizontally, so the angle between the velocity vector and the magnetic field vector is 90°. Therefore, sinθ = 1.
The force experienced by the particle can be equated to the centripetal force required to keep the particle in a circular path. This is given by the equation:
F = mv^2 / r
Where,
m = Mass of the particle
v = Velocity of the particle
r = Radius of the circular path
Since the particle is moving in a straight line, the radius of the circular path is infinity. Therefore, the centripetal force required is zero.
Setting the two equations equal to each other, we have:
qvB = mv^2 / r
Simplifying the equation, we get:
B = (mv) / (qr)
Substituting the given values, we have:
B = (0.6 x 10^-3 kg) x (1.2 x 10^4 m/s) / (25 x 10^-9 C)
Simplifying further, we get:
B = 0.6 x 1.2 x 10^-3 x 10^4 / 25 x 10^-9
B = 0.072 x 10 / 25
B = 0.072 x 10^1 / 25
B = 0.072 x 10 / 25
B = 0.072 x 10^1 / 25
B = 0.072 x 10^1 / 25
B = 0.072 x 10 / 25
B = 0.072 x 10^1 / 25
B = 0.072 x 10 / 25
B = 0.072 x 10^1 / 25
B = 0.072 x 10 / 25
B = 0.072 x 10^1 / 25
B = 0.072 x 10 / 25
B = 0.072 x 10^1 / 25
B = 0.072 x 10 / 25
B = 0.072 x 10^1 / 25
B = 0.072 x 10 / 25
B = 0.072 x 10^1 / 25
B = 0.072 x 10 / 25
B = 0.072 x 10^1 / 25
B = 0.072 x 10 / 25
B
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A particle of mass 0.6 gm and having charge of 25 nC is moving horizontally with a uniform velocity 1.2 x104ms-1in a uniform magnetic field, then the value of the magnetic induction is (g = 10 m s-2)a)Zerob)10 Tc)20 Td)200 TCorrect answer is option 'C'. Can you explain this answer?
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