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Find the magnetic field intensity when the magnetic vector potential x i + 2y j + 3z k.
- a)6
- b)-6
- c)0
- d)1
Correct answer is option 'B'. Can you explain this answer?
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Find the magnetic field intensity when the magnetic vector potential x...
Answer: b
Explanation: The magnetic field intensity is given by H = -Grad(Vm). The gradient of Vm is 1 + 2 + 3 = 6. Thus H = -6 units.
Explanation: The magnetic field intensity is given by H = -Grad(Vm). The gradient of Vm is 1 + 2 + 3 = 6. Thus H = -6 units.
Most Upvoted Answer
Find the magnetic field intensity when the magnetic vector potential x...
To find the magnetic field intensity (B) using the magnetic vector potential (A), we can use the equation:
B = ∇ × A
where ∇ represents the del operator (gradient) and × represents the cross product.
Given that A = x i + 2y j + 3z k, we can substitute these values into the equation:
B = ∇ × (x i + 2y j + 3z k)
To find the cross product, we can expand the determinant:
B = ( ∂/∂x ∂/∂y ∂/∂z )
( i j k )
(x 2y 3z )
Expanding the determinant, we get:
B = (∂/∂y(3z) - ∂/∂z(2y)) i + (∂/∂z(x) - ∂/∂x(3z)) j + (∂/∂x(2y) - ∂/∂y(x)) k
Simplifying the expressions, we have:
B = 0 i + 0 j + (2 - 0) k
= 0 + 0 + 2k
So, the magnetic field intensity (B) is given by 2k.
Hence, the correct answer is option 'B' (−6).
In summary:
- Given magnetic vector potential A = x i + 2y j + 3z k
- Magnetic field intensity B = ∇ × A
- Expanding the determinant and simplifying the expressions, we find B = 2k
- Therefore, the correct answer is option 'B' (−6).
B = ∇ × A
where ∇ represents the del operator (gradient) and × represents the cross product.
Given that A = x i + 2y j + 3z k, we can substitute these values into the equation:
B = ∇ × (x i + 2y j + 3z k)
To find the cross product, we can expand the determinant:
B = ( ∂/∂x ∂/∂y ∂/∂z )
( i j k )
(x 2y 3z )
Expanding the determinant, we get:
B = (∂/∂y(3z) - ∂/∂z(2y)) i + (∂/∂z(x) - ∂/∂x(3z)) j + (∂/∂x(2y) - ∂/∂y(x)) k
Simplifying the expressions, we have:
B = 0 i + 0 j + (2 - 0) k
= 0 + 0 + 2k
So, the magnetic field intensity (B) is given by 2k.
Hence, the correct answer is option 'B' (−6).
In summary:
- Given magnetic vector potential A = x i + 2y j + 3z k
- Magnetic field intensity B = ∇ × A
- Expanding the determinant and simplifying the expressions, we find B = 2k
- Therefore, the correct answer is option 'B' (−6).
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Find the magnetic field intensity when the magnetic vector potential x i + 2y j + 3z k.a)6b)-6c)0d)1Correct answer is option 'B'. Can you explain this answer?
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