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Q)A hollow charged metal sphere has radius r. If the potential difference between its surface and a point at a distance 3r from the centre is V, then the electric field intensity at distance 3r from the centre is (1)V/2r (2)V/6r (3)V/4r (4) V/3r Option 2 is correct !can u explain?
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Q)A hollow charged metal sphere has radius r. If the potential differe...
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Q)A hollow charged metal sphere has radius r. If the potential differe...
Solution:
Given,
Potential difference (V) between the surface of the hollow charged metal sphere and a point at a distance 3r from the centre.
Radius of the metal sphere (r).
To find:
Electric field intensity at a distance 3r from the centre.
As we know that,
Electric field intensity is the negative gradient of the potential difference.
So,
Electric field intensity (E) = - dV/dr
Where,
V = potential difference
r = distance from the centre of sphere.
Now,
Let's consider a Gaussian surface of radius 3r, enclosing the hollow metal sphere.
Using Gauss's law,
Electric flux through the Gaussian surface is given by,
Electric flux (Φ) = (Qenclosed) / ε0
Where,
Qenclosed = charge enclosed by the Gaussian surface
ε0 = permittivity of free space.
As the metal sphere is hollow, the charge enclosed by the Gaussian surface is zero.
Therefore,
Electric flux (Φ) = 0.
Now,
Let's find the electric field intensity at a distance 3r from the centre using the potential difference.
We know that,
Potential difference (V) between the surface of the hollow charged metal sphere and a point at a distance 3r from the centre is given by,
V = (Q / 4πε0r) - (Q / 4πε0(3r))
Where,
Q = charge on the hollow metal sphere.
Simplifying the above equation, we get
V = Q / 4πε0r (1/3 - 1)
V = - Q / 4πε0r (2/3)
V = - (2/3) (Q / 4πε0r)
Now,
Electric field intensity (E) at a distance 3r from the centre is given by,
E = - dV/dr
Differentiating V with respect to r, we get
dV/dr = (2/3) (Q / 4πε0r^2)
Putting the value of Q from the above equation, we get
dV/dr = (2/3) (V / r)
Therefore,
Electric field intensity at a distance 3r from the centre is given by,
E = - dV/dr = - (2/3) (V / r) = - (2/3) (V / 3r) = - V / (3r)
Hence,
Electric field intensity at a distance 3r from the centre is V/6r.
Therefore, the correct option is (2) V/6r.
Given,
Potential difference (V) between the surface of the hollow charged metal sphere and a point at a distance 3r from the centre.
Radius of the metal sphere (r).
To find:
Electric field intensity at a distance 3r from the centre.
As we know that,
Electric field intensity is the negative gradient of the potential difference.
So,
Electric field intensity (E) = - dV/dr
Where,
V = potential difference
r = distance from the centre of sphere.
Now,
Let's consider a Gaussian surface of radius 3r, enclosing the hollow metal sphere.
Using Gauss's law,
Electric flux through the Gaussian surface is given by,
Electric flux (Φ) = (Qenclosed) / ε0
Where,
Qenclosed = charge enclosed by the Gaussian surface
ε0 = permittivity of free space.
As the metal sphere is hollow, the charge enclosed by the Gaussian surface is zero.
Therefore,
Electric flux (Φ) = 0.
Now,
Let's find the electric field intensity at a distance 3r from the centre using the potential difference.
We know that,
Potential difference (V) between the surface of the hollow charged metal sphere and a point at a distance 3r from the centre is given by,
V = (Q / 4πε0r) - (Q / 4πε0(3r))
Where,
Q = charge on the hollow metal sphere.
Simplifying the above equation, we get
V = Q / 4πε0r (1/3 - 1)
V = - Q / 4πε0r (2/3)
V = - (2/3) (Q / 4πε0r)
Now,
Electric field intensity (E) at a distance 3r from the centre is given by,
E = - dV/dr
Differentiating V with respect to r, we get
dV/dr = (2/3) (Q / 4πε0r^2)
Putting the value of Q from the above equation, we get
dV/dr = (2/3) (V / r)
Therefore,
Electric field intensity at a distance 3r from the centre is given by,
E = - dV/dr = - (2/3) (V / r) = - (2/3) (V / 3r) = - V / (3r)
Hence,
Electric field intensity at a distance 3r from the centre is V/6r.
Therefore, the correct option is (2) V/6r.
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Q)A hollow charged metal sphere has radius r. If the potential difference between its surface and a point at a distance 3r from the centre is V, then the electric field intensity at distance 3r from the centre is (1)V/2r (2)V/6r (3)V/4r (4) V/3r Option 2 is correct !can u explain?
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Q)A hollow charged metal sphere has radius r. If the potential difference between its surface and a point at a distance 3r from the centre is V, then the electric field intensity at distance 3r from the centre is (1)V/2r (2)V/6r (3)V/4r (4) V/3r Option 2 is correct !can u explain? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Q)A hollow charged metal sphere has radius r. If the potential difference between its surface and a point at a distance 3r from the centre is V, then the electric field intensity at distance 3r from the centre is (1)V/2r (2)V/6r (3)V/4r (4) V/3r Option 2 is correct !can u explain? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q)A hollow charged metal sphere has radius r. If the potential difference between its surface and a point at a distance 3r from the centre is V, then the electric field intensity at distance 3r from the centre is (1)V/2r (2)V/6r (3)V/4r (4) V/3r Option 2 is correct !can u explain?.
Q)A hollow charged metal sphere has radius r. If the potential difference between its surface and a point at a distance 3r from the centre is V, then the electric field intensity at distance 3r from the centre is (1)V/2r (2)V/6r (3)V/4r (4) V/3r Option 2 is correct !can u explain? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Q)A hollow charged metal sphere has radius r. If the potential difference between its surface and a point at a distance 3r from the centre is V, then the electric field intensity at distance 3r from the centre is (1)V/2r (2)V/6r (3)V/4r (4) V/3r Option 2 is correct !can u explain? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q)A hollow charged metal sphere has radius r. If the potential difference between its surface and a point at a distance 3r from the centre is V, then the electric field intensity at distance 3r from the centre is (1)V/2r (2)V/6r (3)V/4r (4) V/3r Option 2 is correct !can u explain?.
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