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Two non conducting spherical shellsare uniformly charged .one shell S1 having radius 5 m and charge -2 micro coloumb has a centre at (-1,2,-1)and the other shell S2 has a radius 6 m and charge 3micro coloumb and centre at (-2,1,-1).FindFind the electric field(in vector form) at point (1,-1,3)?
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Two non conducting spherical shellsare uniformly charged .one shell S1...
Problem Statement:
Two non-conducting spherical shells are uniformly charged. One shell S1 having radius 5 m and charge -2 micro coulombs has a centre at (-1, 2, -1) and the other shell S2 has a radius 6 m and charge 3 micro coulombs and centre at (-2, 1, -1). Find the electric field (in vector form) at point (1, -1, 3).
Solution:
Step 1: Calculate the electric field due to each shell separately.
We know that the electric field due to a uniformly charged spherical shell is given by:
E = kQ/r^2
where k is the Coulomb constant, Q is the charge on the shell and r is the distance from the centre of the shell.
Electric field due to S1:
E1 = kQ1/r1^2
= (9x10^9 Nm^2/C^2)(-2x10^-6 C)/(5m)^2
= -72x10^3 N/C
Electric field due to S2:
E2 = kQ2/r2^2
= (9x10^9 Nm^2/C^2)(3x10^-6 C)/(6m)^2
= 22.5x10^3 N/C
Step 2: Calculate the distance and unit vector from the point P(1, -1, 3) to the centres of the shells.
Distance from P to the centre of S1:
r1 = ((-1-1)^2 + (2+1)^2 + (-1-3)^2)^(1/2)
= 4.36 m
Distance from P to the centre of S2:
r2 = ((-2-1)^2 + (1+1)^2 + (-1-3)^2)^(1/2)
= 5.92 m
Unit vector from P to the centre of S1:
v1 = (1, -1, 3) - (-1, 2, -1)
= (2, -3, 4)
v1_hat = v1/|v1|
= (2/7, -3/7, 4/7)
Unit vector from P to the centre of S2:
v2 = (1, -1, 3) - (-2, 1, -1)
= (3, -2, 4)
v2_hat = v2/|v2|
= (3/7, -2/7, 4/7)
Step 3: Calculate the net electric field at point P.
The net electric field at point P due to both shells is given by the vector sum of the electric fields due to each shell:
E_net = E1*v1_hat + E2*v2_hat
= (-72x10^3 N/C)(2/7, -3/7, 4/7) + (22.5x10^3 N/C)(3/7, -2/7, 4/7)
= (-13.7x10^3 N/C, 16.3x10^3
Two non-conducting spherical shells are uniformly charged. One shell S1 having radius 5 m and charge -2 micro coulombs has a centre at (-1, 2, -1) and the other shell S2 has a radius 6 m and charge 3 micro coulombs and centre at (-2, 1, -1). Find the electric field (in vector form) at point (1, -1, 3).
Solution:
Step 1: Calculate the electric field due to each shell separately.
We know that the electric field due to a uniformly charged spherical shell is given by:
E = kQ/r^2
where k is the Coulomb constant, Q is the charge on the shell and r is the distance from the centre of the shell.
Electric field due to S1:
E1 = kQ1/r1^2
= (9x10^9 Nm^2/C^2)(-2x10^-6 C)/(5m)^2
= -72x10^3 N/C
Electric field due to S2:
E2 = kQ2/r2^2
= (9x10^9 Nm^2/C^2)(3x10^-6 C)/(6m)^2
= 22.5x10^3 N/C
Step 2: Calculate the distance and unit vector from the point P(1, -1, 3) to the centres of the shells.
Distance from P to the centre of S1:
r1 = ((-1-1)^2 + (2+1)^2 + (-1-3)^2)^(1/2)
= 4.36 m
Distance from P to the centre of S2:
r2 = ((-2-1)^2 + (1+1)^2 + (-1-3)^2)^(1/2)
= 5.92 m
Unit vector from P to the centre of S1:
v1 = (1, -1, 3) - (-1, 2, -1)
= (2, -3, 4)
v1_hat = v1/|v1|
= (2/7, -3/7, 4/7)
Unit vector from P to the centre of S2:
v2 = (1, -1, 3) - (-2, 1, -1)
= (3, -2, 4)
v2_hat = v2/|v2|
= (3/7, -2/7, 4/7)
Step 3: Calculate the net electric field at point P.
The net electric field at point P due to both shells is given by the vector sum of the electric fields due to each shell:
E_net = E1*v1_hat + E2*v2_hat
= (-72x10^3 N/C)(2/7, -3/7, 4/7) + (22.5x10^3 N/C)(3/7, -2/7, 4/7)
= (-13.7x10^3 N/C, 16.3x10^3
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Two non conducting spherical shellsare uniformly charged .one shell S1 having radius 5 m and charge -2 micro coloumb has a centre at (-1,2,-1)and the other shell S2 has a radius 6 m and charge 3micro coloumb and centre at (-2,1,-1).FindFind the electric field(in vector form) at point (1,-1,3)?
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Two non conducting spherical shellsare uniformly charged .one shell S1 having radius 5 m and charge -2 micro coloumb has a centre at (-1,2,-1)and the other shell S2 has a radius 6 m and charge 3micro coloumb and centre at (-2,1,-1).FindFind the electric field(in vector form) at point (1,-1,3)? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two non conducting spherical shellsare uniformly charged .one shell S1 having radius 5 m and charge -2 micro coloumb has a centre at (-1,2,-1)and the other shell S2 has a radius 6 m and charge 3micro coloumb and centre at (-2,1,-1).FindFind the electric field(in vector form) at point (1,-1,3)? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two non conducting spherical shellsare uniformly charged .one shell S1 having radius 5 m and charge -2 micro coloumb has a centre at (-1,2,-1)and the other shell S2 has a radius 6 m and charge 3micro coloumb and centre at (-2,1,-1).FindFind the electric field(in vector form) at point (1,-1,3)?.
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