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From a point charge, there is a fixed point A. At A, there is an electric field of 500 V/m andpotential difference of 3000 V. Distance betweenpoint charge and A will be [1997]
- a)6 m
- b)12 m
- c)16 m
- d)24 m
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
From a point charge, there is a fixed point A. At A, there is an elect...
Given : Electric field (E) = 500 V/m
and potential difference (V) = 3000 V.
We know that electric field
and potential difference (V) = 3000 V.
We know that electric field
[where d = Distance between point charge
and A]
and A]
Most Upvoted Answer
From a point charge, there is a fixed point A. At A, there is an elect...
Given: Electric field at point A, E = 500 V/m
Potential difference between point charge and A, V = 3000 V
To find: Distance between point charge and A
Formulae:
Electric field due to a point charge, E = kq/r²
Potential difference due to a point charge, V = kq/r
where k = Coulomb's constant = 9 × 10^9 Nm²/C²
q = charge of the point charge in Coulombs
r = distance between point charge and point A in meters
Solution:
We can use the formula for potential difference to find the value of q/r.
V = kq/r
=> q/r = V/k
=> q/r = (3000)/(9 × 10^9)
=> q/r = 1/3 × 10^-6 C/m
Now, we can use the formula for electric field to find the value of r.
E = kq/r²
=> r² = kq/E
=> r² = (9 × 10^9) × (1/3 × 10^-6)/500
=> r² = 6
=> r = sqrt(6) = 2.45 m (approx)
Therefore, the distance between point charge and A is approximately 2.45 m, which is closest to option (a) 6 m.
Potential difference between point charge and A, V = 3000 V
To find: Distance between point charge and A
Formulae:
Electric field due to a point charge, E = kq/r²
Potential difference due to a point charge, V = kq/r
where k = Coulomb's constant = 9 × 10^9 Nm²/C²
q = charge of the point charge in Coulombs
r = distance between point charge and point A in meters
Solution:
We can use the formula for potential difference to find the value of q/r.
V = kq/r
=> q/r = V/k
=> q/r = (3000)/(9 × 10^9)
=> q/r = 1/3 × 10^-6 C/m
Now, we can use the formula for electric field to find the value of r.
E = kq/r²
=> r² = kq/E
=> r² = (9 × 10^9) × (1/3 × 10^-6)/500
=> r² = 6
=> r = sqrt(6) = 2.45 m (approx)
Therefore, the distance between point charge and A is approximately 2.45 m, which is closest to option (a) 6 m.
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