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On a thin rod of length l=1m lying on X axis with one end at origin (0,0) there is a uniformly distributed charge per unit length given by lambda =Kx where K=10^-9Cm2.The work done in displacing a charge q=1000microC from point A0,0.66) to B(0,1) is?
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On a thin rod of length l=1m lying on X axis with one end at origin (0...
Problem: Find the work done in displacing a charge q=1000microC from point A(0,0.66) to B(0,1) on a thin rod of length l=1m lying on X axis with uniformly distributed charge per unit length given by lambda =Kx where K=10^-9Cm2.
Solution:
Step 1: Calculation of Charge Density
The charge density along the rod is given by lambda = Kx, where K = 10^-9 Cm^2.
At x = 0.66m, the charge density is given by:
lambda = Kx = (10^-9)(0.66) = 6.6 x 10^-10 C/m
At x = 1m, the charge density is given by:
lambda = Kx = (10^-9)(1) = 10^-9 C/m
Step 2: Calculation of Electric Field
The electric field at point A(0,0.66) due to the rod is given by:
dE = k(lambda)(dx)/r^2
where k is the Coulomb constant, dx is the length of the element, and r is the distance between the element and the point A.
dE = (9 x 10^9 Nm^2/C^2)(6.6 x 10^-10 C/m)(0.01 m)/(0.66^2 + 0.01)^(3/2)
dE = 2.12 x 10^4 N/C
The electric field at point B(0,1) due to the rod is given by:
dE = k(lambda)(dx)/r^2
dE = (9 x 10^9 Nm^2/C^2)(10^-9 C/m)(0.01 m)/(1^2 + 0.01)^(3/2)
dE = 8.98 x 10^3 N/C
Step 3: Calculation of Work Done
The work done in moving the charge q from point A to B is given by:
W = q(VB - VA)
where VB and VA are the potentials at points B and A, respectively.
VB - VA = -Ed
where d is the distance between points A and B.
d = sqrt[(0 - 0)^2 + (1 - 0.66)^2] = 0.34 m
VB - VA = -(2.12 x 10^4 N/C)(0.34 m)
VB - VA = -7.22 x 10^3 V
W = (1000 x 10^-6 C)(-7.22 x 10^3 V)
W = -7.22 x 10^-3 J
Therefore, the work done in moving the charge q from point A to B is -7.22 x 10^-3 J.
Solution:
Step 1: Calculation of Charge Density
The charge density along the rod is given by lambda = Kx, where K = 10^-9 Cm^2.
At x = 0.66m, the charge density is given by:
lambda = Kx = (10^-9)(0.66) = 6.6 x 10^-10 C/m
At x = 1m, the charge density is given by:
lambda = Kx = (10^-9)(1) = 10^-9 C/m
Step 2: Calculation of Electric Field
The electric field at point A(0,0.66) due to the rod is given by:
dE = k(lambda)(dx)/r^2
where k is the Coulomb constant, dx is the length of the element, and r is the distance between the element and the point A.
dE = (9 x 10^9 Nm^2/C^2)(6.6 x 10^-10 C/m)(0.01 m)/(0.66^2 + 0.01)^(3/2)
dE = 2.12 x 10^4 N/C
The electric field at point B(0,1) due to the rod is given by:
dE = k(lambda)(dx)/r^2
dE = (9 x 10^9 Nm^2/C^2)(10^-9 C/m)(0.01 m)/(1^2 + 0.01)^(3/2)
dE = 8.98 x 10^3 N/C
Step 3: Calculation of Work Done
The work done in moving the charge q from point A to B is given by:
W = q(VB - VA)
where VB and VA are the potentials at points B and A, respectively.
VB - VA = -Ed
where d is the distance between points A and B.
d = sqrt[(0 - 0)^2 + (1 - 0.66)^2] = 0.34 m
VB - VA = -(2.12 x 10^4 N/C)(0.34 m)
VB - VA = -7.22 x 10^3 V
W = (1000 x 10^-6 C)(-7.22 x 10^3 V)
W = -7.22 x 10^-3 J
Therefore, the work done in moving the charge q from point A to B is -7.22 x 10^-3 J.
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On a thin rod of length l=1m lying on X axis with one end at origin (0,0) there is a uniformly distributed charge per unit length given by lambda =Kx where K=10^-9Cm2.The work done in displacing a charge q=1000microC from point A0,0.66) to B(0,1) is?
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On a thin rod of length l=1m lying on X axis with one end at origin (0,0) there is a uniformly distributed charge per unit length given by lambda =Kx where K=10^-9Cm2.The work done in displacing a charge q=1000microC from point A0,0.66) to B(0,1) is? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about On a thin rod of length l=1m lying on X axis with one end at origin (0,0) there is a uniformly distributed charge per unit length given by lambda =Kx where K=10^-9Cm2.The work done in displacing a charge q=1000microC from point A0,0.66) to B(0,1) is? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for On a thin rod of length l=1m lying on X axis with one end at origin (0,0) there is a uniformly distributed charge per unit length given by lambda =Kx where K=10^-9Cm2.The work done in displacing a charge q=1000microC from point A0,0.66) to B(0,1) is?.
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