Question:
Which theorem relates the line integral of a vector field over a closed curve to the surface integral of the curl of the field over the surface bounded by the curve?
Which theorem relates the line integral of a vector field over a closed curve to the surface integral of the curl of the field over the surface bounded by the curve?
Show Hint
Stokes's theorem connects the circulation of a vector field along a curve to the curl of the field over the surface enclosed by the curve.
Updated On: May 5, 2025
- Stokes's theorem
- Gauss's theorem
- Green's theorem
- Divergence theorem
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Stokes's theorem relates the line integral of a vector field over a closed curve to the surface integral of the curl of the field over the surface bounded by the curve. This theorem is fundamental in vector calculus and is used in various fields such as electromagnetism.
Was this answer helpful?
0
0
Top Questions on Vector Calculus
- Consider a vector \(\mathbf{F} = \frac{1}{\pi}[-\sin y \hat{i} + x(1 - \cos y)\hat{j}]\). The value of the integral \(\oint \mathbf{F} \cdot d\mathbf{r}\) over a circle \(x^2 + y^2 = 1\) evaluated in the anti-clockwise direction is _____. (in integer)
- IIT JAM PHY - 2025
- Physics
- Vector Calculus
- In Cartesian coordinates, consider the functions \(u(x, y) = \frac{1{2}(x^2 - y^2)\) and \(v(x,y) = xy\). If \((r, \theta)\) are the polar coordinates, the Jacobian determinant \(|\frac{\partial(u,v)}{\partial(r,\theta)}|\) is}
- IIT JAM PHY - 2025
- Mathematics
- Vector Calculus
- Given a function \(f(x, y) = \frac{x}{a}e^y + \frac{y}{b}e^x\), where \(x = at\) and \(y = bt\) (a and b are non-zero constants), the value of \(\frac{df}{dt}\) at \(t = 0\) is
- IIT JAM PHY - 2025
- Mathematics
- Vector Calculus
- Which one of the following figures represents the vector field \(\mathbf{A} = y\hat{i}\)?
(\(\hat{i}\) is the unit vector along the x-direction)- IIT JAM PHY - 2025
- Mathematics
- Vector Calculus
- Consider a volume V enclosed by a closed surface S having unit surface normal \(\hat{n}\). For \(\mathbf{r} = x\hat{i} + y\hat{j} + z\hat{k}\), the value of the surface integral \(\frac{1}{9} \oint_{S} \mathbf{r} \cdot \hat{n} \,dS\) is
- IIT JAM PHY - 2025
- Mathematics
- Vector Calculus
View More Questions
Questions Asked in AP PGECET exam
- The multiple access method used in Global Positioning Systems is ________.
- AP PGECET - 2025
- Digital Electronics and Logic Gates
- National Remote Sensing Day is celebrated on ________ every year.
- AP PGECET - 2025
- Remote Sensor
- SDI stands for
- AP PGECET - 2025
- Remote Sensor
- Suppose \( R_1 \) and \( R_2 \) are reflexive relations on a set \( A \). Which of the following statements is correct?
- AP PGECET - 2025
- Set Theory
- Determine the value of $\lambda$ and $\mu$ for which the system of equations
$x + 2y + z = 6$,
$x + 4y + 3z = 10$,
$2x + 4y + \lambda z = \mu$
has a unique solution.- AP PGECET - 2025
- Linear Algebra
View More Questions