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Question
An isolated point charge particle produces an electric field `vecE` at a point 3 m away from it. The distance of the point at which the field is `vecE/4` will be ______.
Options
2 m
3 m
4 m
6 m
Solution
An isolated point charge particle produces an electric field `vecE` at a point 3 m away from it. The distance of the point at which the field is `vecE/4` will be 6 m.
Explanation:
The electric field E produced by a point charge at a distance r from it is given by the equation:
E = `(kQ)/r^2`
Where k is Coulomb's constant and Q is the charge on the particle.
Let the distance of the point where the electric field is `E/4` be x metres away from the particle.
So, the electric field at this point can be calculated as:
`E/4 = (kQ)/x^2`
Also, we know that the electric field at a point 3 metres away from the particle is E. So we can write:
`E = (kQ)/3^2`
Equating these two equations, we get:
`(kQ)/x^2 = (kQ)/(3^2 xx 4)`
In simplification, we get:
`x^2 = 3^2 xx 4`
`x^2 = 36`
Taking the square root of both sides, we get:
x = 6
Therefore, the distance of the point where the electric field is `E/4` is 6 metres away from the particles.
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