Recent content by catch22

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    Finding Area with Double Integrals: What is the Approach for This Homework?

    Homework Statement Homework EquationsThe Attempt at a Solution here is my approach, I take the whole area, which is π16 then subtract the unshaded region now to find the unshaded region's area, I use rectangular coordinates. my bounds are from -2 to 2 for x and the the top and bottom of...
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    Rec, Spherical and cylind coordinates.

    Homework Statement Homework EquationsThe Attempt at a Solutionhere is the setup for each, can someone check if they are correct before I evaluate the volume?
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    How does a dielectric affect the capacitance of a capacitor?

    whoops, for Ceq = C1 + C2 + C3... in parallel Ceq = 1/C1 + 1/C2 + 1/C3... in series
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    How does a dielectric affect the capacitance of a capacitor?

    in series, Q is constant through out. Parallel , V is constant through out.
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    How does a dielectric affect the capacitance of a capacitor?

    Another question: Could someone explain this to me? Answer key says C. I thought in series, Ceq = C1 + C2 + C3... and in parallel Ceq = 1/C1 + 1/C2 + 1/C3...
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    How does a dielectric affect the capacitance of a capacitor?

    Homework Statement Homework EquationsThe Attempt at a Solution for #14, I remember a battery maintains the potential therefore, V should be constant; dielectric increases charge on plates and increases capacitance but I couldn't find an option that matched. The answer key says "d" but I...
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    Physics concept questions (electric field & potential diff.)

    If the field doesn't change, then V should decrease as d decreases. but why do we treat the plates as if they were infinitely long? say the plates are 1 meter long, each, would the field still remain the same?
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    Physics concept questions (electric field & potential diff.)

    __________________________________________________________________________________________________________________ Here is how I picture this: using V=Ed, since V is constant, and the distance between the slab of metal and each plate is d/4, E should increase.
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    Physics concept questions (electric field & potential diff.)

    #2) ____________________________________________________________________________________________________ #2a) the battery maintains the electric potential in each plate so the potential difference should remain the same. #2b) using V = Ed, if V is constant, d is decreased, E should increase...
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    Physics concept questions (electric field & potential diff.)

    Homework Statement Homework EquationsThe Attempt at a Solution 1) charges should remain the same since there is no path for them to go anyway. 2) Now, if the panels were of infinite length, I believe the electric field should be the same regardless of distance? But in this case, the panels...
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    Equation of normal line and tangent plane

    √2y- 2 - z + 2 = 0 √2y - z = 0
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    Finding a point on a surface which is closest to given point

    curious to see which way is method, I haven't learned that yet.
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    Linear Approximation of z2 = xy + y + 3 at (0,6,-3)

    so you comparing it to the actual change? which should be final - initial : F(-0.01, 6.01, -2.98) - F(0,6, -3)
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    How Can We Determine ∂z/∂r for a Complex Multivariable Equation?

    Homework Statement If z= x2 - y2 + xy x = w + 4t y = w2 -5t + 4 w = r2 - 5u t = 3r + 5u find ∂z/∂r Homework EquationsThe Attempt at a Solution This is going to be quite long and tedious so bare with me, but here is my work. drawing a diagram to help out a bit. ∂z/∂r =...
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    Linear Approximation of z2 = xy + y + 3 at (0,6,-3)

    Homework Statement Find linear approximation of the surface z2 = xy + y + 3 at the point (0,6, -3) and use it to approximate f(-0.01, 6.01, -2.98) Homework EquationsThe Attempt at a Solution [/B] so this means the total surface has decrease by -0.17?