A charged sphere of mass 0.6 g and charge 4 μ C is placed in a uniform electric field. The sphere is released from rest in the field and travels a distance 13 cm in 0.5 seconds. Calculate the strength of the magnetic field.
Answers
Answer:
Solution
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Correct option is D)
Force on particle=F=qE in opposite direction of motion
And, F=ma=qE
⟹a=
m
qE
=
10
−3
5×10
−6
×2×10
5
⟹a=10
3
m/s
2
and this acceleration is negative since particle is thrown against force.
And final velocity is v=0
Using v
2
−u
2
=2as
⟹0−20
2
=−2×1000×s
⟹s=0.2m
Answer-(D)
The strength of the magnetic field is 5.2 x 10^-11 T.
To find,
The strength of the magnetic field.
Given,
A charged sphere of mass 0.6 g
Charge 4 μ C is placed in a uniform electric field.
Distance traveled 13 cm in 0.5 seconds
Solution,
The motion of the charged sphere in the uniform electric field is given by:
qE = m a
where q is the charge of the sphere, E is the strength of the electric field, m is the mass of the sphere, and a is the acceleration of the sphere.
The distance traveled by the sphere can be calculated using the formula for the distance traveled with constant acceleration:
d = 1/2 a t^2
where d is the distance traveled, t is the time taken, and a is the acceleration.
We are given that the sphere traveled a distance of 13 cm in 0.5 seconds. Therefore, we can calculate the acceleration of the sphere as:
a = 2 d / t^2 = 2 * 0.13 m / (0.5 s)^2 = 1.04 m/s^2
Substituting this into the equation for the motion of the charged sphere, we get:
E = m a / q = (0.6 g / 1000) * (1.04 m/s^2) / (4 μC) = 0.0156 N/C
The strength of the magnetic field can be calculated using the formula:
B = E / c
where c is the speed of light. Substituting the value of E, we get:
B = 0.0156 N/C / 3 x 10^8 m/s = 5.2 x 10^-11 T
Therefore, the strength of the magnetic field is 5.2 x 10^-11 T.
For further reference about the strength of the magnetic field,
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