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Find the vector potential when the field intensity 60x2 varies from (0,0,0) to (1,0,0).
- a)120
- b)-20
- c)-180
- d)60
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Find the vector potential when the field intensity 60x2varies from (0,...
Answer: b
Explanation: The field intensity H = -Grad(V). To get V, integrate H with respect to the variable. Thus V = -∫H.dl = -∫60x2 dx = -20x3 as x = 0->1 to get -20.
Explanation: The field intensity H = -Grad(V). To get V, integrate H with respect to the variable. Thus V = -∫H.dl = -∫60x2 dx = -20x3 as x = 0->1 to get -20.
Most Upvoted Answer
Find the vector potential when the field intensity 60x2varies from (0,...
To find the vector potential for a given field intensity, we can use the formula:
A = ∫B.dl
where A is the vector potential, B is the magnetic field intensity, and dl is the differential length along the path of integration.
In this case, the field intensity is given as 60x^2, where x varies from (0,0,0) to (1,0,0).
Let's find the vector potential step by step:
1. Define the path of integration:
The path of integration is the line segment from (0,0,0) to (1,0,0).
2. Parameterize the path:
Let's parameterize the path with respect to x. We can define x as a function of a parameter t such that x = t, y = 0, and z = 0. The parameter t varies from 0 to 1.
3. Calculate the differential length dl:
Since dx = dt, dy = 0, and dz = 0, the differential length dl can be written as dl = dx = dt.
4. Calculate the magnetic field intensity B:
Given B = 60x^2, we substitute x = t into the equation to get B = 60t^2.
5. Calculate the vector potential A:
Using the formula A = ∫B.dl, we have:
A = ∫(60t^2)(dt) from t = 0 to t = 1
= 60∫t^2 dt from 0 to 1
= 60[t^3/3] from 0 to 1
= 60(1/3 - 0)
= 60/3
= 20
Therefore, the vector potential A for the given field intensity is 20.
A = ∫B.dl
where A is the vector potential, B is the magnetic field intensity, and dl is the differential length along the path of integration.
In this case, the field intensity is given as 60x^2, where x varies from (0,0,0) to (1,0,0).
Let's find the vector potential step by step:
1. Define the path of integration:
The path of integration is the line segment from (0,0,0) to (1,0,0).
2. Parameterize the path:
Let's parameterize the path with respect to x. We can define x as a function of a parameter t such that x = t, y = 0, and z = 0. The parameter t varies from 0 to 1.
3. Calculate the differential length dl:
Since dx = dt, dy = 0, and dz = 0, the differential length dl can be written as dl = dx = dt.
4. Calculate the magnetic field intensity B:
Given B = 60x^2, we substitute x = t into the equation to get B = 60t^2.
5. Calculate the vector potential A:
Using the formula A = ∫B.dl, we have:
A = ∫(60t^2)(dt) from t = 0 to t = 1
= 60∫t^2 dt from 0 to 1
= 60[t^3/3] from 0 to 1
= 60(1/3 - 0)
= 60/3
= 20
Therefore, the vector potential A for the given field intensity is 20.
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