Post on 24-Jan-2017
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Uniform Charged ring has radius length a
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a
Uniform Charged ring has radius length a
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Total charge of ring is Q
Uniform Charged ring has total charge Q
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a
Uniform Charged ring has radius length a
+
Total charge of ring is Q
Uniform Charged ring has total charge Q
P
P is a point lying a distance X from center C
X
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a
Uniform Charged ring has radius length a
+
Total charge of ring is Q
Uniform Charged ring has total charge Q
P
P is a point lying a distance X from center
X
Solution:
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a
Uniform Charged ring has radius length a
+
Total charge of ring is Q
Uniform Charged ring has total charge Q
P
P is a point lying a distance X from center
X
Solution:
Take a small charged segment from charged ringdq is charge of small segment
dq
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a
Uniform Charged ring has radius length a
+
Total charge of ring is Q
Uniform Charged ring has total charge Q
P
P is a point lying a distance X from center
X
Solution:
Take a small charged segment from charged ringdq is charge of small segment r is distance between small segment and P
dq
r
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a
Uniform Charged ring has radius length a
+
Total charge of ring is Q
Uniform Charged ring has total charge Q
P
P is a point lying a distance X from center
X
Solution:
Take a small charged segment from charged ringdq is charge of small segment r is distance between small segment and Pr² = a² + X²
dq
r
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+
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a
Uniform Charged ring has radius length a
+
Total charge of ring is Q
Uniform Charged ring has total charge Q
P
P is a point lying a distance X from center
X
Solution:
Take a small charged segment from charged ringdq is charge of small segment r is distance between small segment and Pr² = a² + X² dE is electric field at P due to small
segment
dE = k dq /r²dq
r
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+
+
+
+
a
Uniform Charged ring has radius length a
+
Total charge of ring is Q
Uniform Charged ring has total charge Q
P
P is a point lying a distance X from center
X
Solution:
Take a small charged segment from charged ringdq is charge of small segment r is distance between small segment and Pr² = a² + X² dE is electric field at P due to small
segment
dE = k dq /r²dq
r
dE
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+
+
+
+
+
+
a
Uniform Charged ring has radius length a
+
Total charge of ring is Q
Uniform Charged ring has total charge Q
P
P is a point lying a distance X from center
X
Solution:
Take a small charged segment from charged ringdq is charge of small segment r is distance between small segment and Pr² = a² + X² dE is electric field at P due to small
segment
dE = k dq /r²dq
r
dE
Ө
Ө X - axis
Y - axis
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+
+
+
+
+
+
a
Uniform Charged ring has radius length a
+
Total charge of ring is Q
Uniform Charged ring has total charge Q
P
P is a point lying a distance X from center
X
Solution:
Take a small charged segment from charged ringdq is charge of small segment r is distance between small segment and Pr² = a² + X² dE is electric field at P due to small
segment
dE = k dq /r²dq
r
dE
Ө dE cos ӨӨ X - axis
Y - axis
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+
+
+
+
+
+
a
Uniform Charged ring has radius length a
+
Total charge of ring is Q
Uniform Charged ring has total charge Q
P
P is a point lying a distance X from center
X
Solution:
Take a small charged segment from charged ringdq is charge of small segment r is distance between small segment and Pr² = a² + X² dE is electric field at P due to small
segment
dE = k dq /r²dq
r
dE
Ө dE cos Ө = dEᵪӨ X - axis
Y - axis
+
+
+
+
+
+
+
a
Uniform Charged ring has radius length a
+
Total charge of ring is Q
Uniform Charged ring has total charge Q
P
P is a point lying a distance X from center
X
Solution:
Take a small charged segment from charged ringdq is charge of small segment r is distance between small segment and Pr² = a² + X² dE is electric field at P due to small
segment
dE = k dq /r²dq
r
dE
Ө dE cos Ө = dEᵪӨ X - axis
dEY - axis
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+
+
+
+
+
+
a
Uniform Charged ring has radius length a
+
Total charge of ring is Q
Uniform Charged ring has total charge Q
P
P is a point lying a distance X from center
X
Solution:
Take a small charged segment from charged ringdq is charge of small segment r is distance between small segment and Pr² = a² + X² dE is electric field at P due to small
segment
dE = k dq /r²dq
r
dE
Ө dE cos Ө = dEᵪӨ X - axis
dE = ZeroY - axis
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+
+
+
+
+
+
a
Uniform Charged ring has radius length a
+
Total charge of ring is Q
Uniform Charged ring has total charge Q
P
P is a point lying a distance X from center
X
Solution:
Take a small charged segment from charged ringdq is charge of small segment r is distance between small segment and Pr² = a² + X² dE is electric field at P due to small
segment
dE = k dq /r²
dEᵪ = dE cos Ө = (k dq /r²) . X/r
dq
r
dE
Ө dE cos Ө = dEᵪӨ X - axis
dE = ZeroY - axis
+
+
+
+
+
+
+
a
Uniform Charged ring has radius length a
+
Total charge of ring is Q
Uniform Charged ring has total charge Q
P
P is a point lying a distance X from center
X
Solution:
Take a small charged segment from charged ringdq is charge of small segment r is distance between small segment and Pr² = a² + X² dE is electric field at P due to small
segment
dE = k dq /r²
dEᵪ = dE cos Ө = (k dq /r²) . X/r
dq
r
dE
Ө dE cos Ө = dEᵪӨ X - axis
dE = ZeroY - axis
NB: r² = a² + X²
+
+
+
+
+
+
+
a
Uniform Charged ring has radius length a
+
Total charge of ring is Q
Uniform Charged ring has total charge Q
P
P is a point lying a distance X from center
X
Solution:
Take a small charged segment from charged ringdq is charge of small segment r is distance between small segment and Pr² = a² + X² dE is electric field at P due to small
segment
dE = k dq /r²
dEᵪ = dE cos Ө = (k dq /r²) . X/r
dq
r
dE
Ө dE cos Ө = dEᵪӨ X - axis
dE = ZeroY - axis
NB: r² = a² + X²and r = (a² + X²)²
Explain: The total electric field “E” of uniform charged ring of radius “a” at point “P” is electric field on
the X-axis “Eᵪ”Or
In case of uniform charged ring The Resultant of electric field at point “P” must lie along theX-axis (i.e. Eᵪ is the resultant field)
Answer:The perpendicular component of the electric field created by any charge element is canceled by the perpendicular component of the electric field created by an element on the opposite
side of charged ring.
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a
+P
dq₁
dE₁X - axis
Y - axis
dq₂
dE₂
Ө
dE₁ sin Ө
dE₂ sin Ө
Ө
Ө
Ө
Suppose a negative charge is placed at the center of the ring and displaced slightly by a distance x << a along X-axis. What type of motion dose it exhibit?
Electric Field Lines: