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Find the divergence of the field, P = x2yz i + xz k
- a)xyz + 2x
- b)2xyz + x
- c)xyz + 2z
- d)2xyz + z
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Find the divergence of the field, P = x2yz i + xz ka)xyz + 2xb)2xyz + ...
Answer: b
Explanation: Div(P) = Dx(x2yz) + Dy(0) + Dz(xz) = 2xyz + x, which is option b. For different values of x,y,z the divergence of the field varies.
Explanation: Div(P) = Dx(x2yz) + Dy(0) + Dz(xz) = 2xyz + x, which is option b. For different values of x,y,z the divergence of the field varies.
Most Upvoted Answer
Find the divergence of the field, P = x2yz i + xz ka)xyz + 2xb)2xyz + ...
Divergence of the given field P can be found using the formula:
div(P) = ∂Px/∂x + ∂Py/∂y + ∂Pz/∂z
where Px, Py, and Pz are the x, y, and z components of the field, respectively.
Breaking down the given field into its components, we get:
Px = x^2yz
Py = xz
Pz = xyz
Now, let's find the partial derivatives of each component:
∂Px/∂x = 2xyz
∂Py/∂y = 0
∂Pz/∂z = xy
Adding these partial derivatives, we get:
div(P) = 2xyz + 0 + xy
Simplifying this expression, we get:
div(P) = 2xyz + xy
Comparing this with the given options, we can see that the correct answer is option B, which is 2xyz.
div(P) = ∂Px/∂x + ∂Py/∂y + ∂Pz/∂z
where Px, Py, and Pz are the x, y, and z components of the field, respectively.
Breaking down the given field into its components, we get:
Px = x^2yz
Py = xz
Pz = xyz
Now, let's find the partial derivatives of each component:
∂Px/∂x = 2xyz
∂Py/∂y = 0
∂Pz/∂z = xy
Adding these partial derivatives, we get:
div(P) = 2xyz + 0 + xy
Simplifying this expression, we get:
div(P) = 2xyz + xy
Comparing this with the given options, we can see that the correct answer is option B, which is 2xyz.
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