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Find the force between 2C and -1C separated by a distance 1m in air(in newton).
To find the force between two charges, we can use Coulomb's law, which is given by the formula:[F = k frac{|q_1 q_2|}{r^2}]Where:- (F) is the force between the charges,- (k) is Coulomb's constant ((8.99 times 10^9 , text{N m}^2/text{C}^2)),- (q_1) and (q_2) are the amounts of the charges,- (r) is thRead more
To find the force between two charges, we can use Coulomb’s law, which is given by the formula:
[
F = k frac{|q_1 q_2|}{r^2}
]
Where:
– (F) is the force between the charges,
– (k) is Coulomb’s constant ((8.99 times 10^9 , text{N m}^2/text{C}^2)),
– (q_1) and (q_2) are the amounts of the charges,
– (r) is the distance separating the charges.
Given:
– (q_1 = 2 , text{C}),
– (q_2 = -1 , text{C}),
– (r = 1 , text{m}).
Substituting these values into the formula:
[
F = 8.99 times 10^9 frac{|2 times (-1)|}{1^2}
]
[
F = 8.99 times 10^9 frac{2}{1}
]
[
F = 8.99 times 10^9 times 2
]
[
F = 17.98 times 10^9 , text{N}
]
Since the charges have opposite signs, the force will be attractive.
Therefore
See lessCoulomb is the unit of which quantity?
Coulomb is the unit of electric charge.
Coulomb is the unit of electric charge.
See lessWhat is the relation of the input voltage with the magnetic flux?
The relation of the input voltage (V) with the magnetic flux (Φ) in a coil is described by Faraday's Law of Electromagnetic Induction. According to this law, the induced voltage in a coil is proportional to the rate of change of magnetic flux through the coil. Mathematically, it can be expressed as:Read more
The relation of the input voltage (V) with the magnetic flux (Φ) in a coil is described by Faraday’s Law of Electromagnetic Induction. According to this law, the induced voltage in a coil is proportional to the rate of change of magnetic flux through the coil. Mathematically, it can be expressed as:
[ V = -frac{dΦ}{dt} ]
where:
– ( V ) is the induced voltage,
– ( Φ ) is the magnetic flux, and
– ( frac{dΦ}{dt} ) is the rate of change of magnetic flux over time.
The negative sign indicates the direction of the induced voltage, as described by Lenz’s Law, which states that the induced voltage will be in a direction that opposes the change in magnetic flux.
See lessDivergence theorem computes to zero for a solenoidal function. State True/False.
True
True
See lessFor a function given by F = 4x i + 7y j +z k, the divergence theorem evaluates to which of the values given, if the surface considered is a cone of radius 1/2π m and height 4π2 m.
To apply the divergence theorem to the vector field ( mathbf{F} = 4x mathbf{i} + 7y mathbf{j} + z mathbf{k} ), we first need to calculate the divergence of ( mathbf{F} ).The divergence ( nabla cdot mathbf{F} ) is calculated as follows:[nabla cdot mathbf{F} = frac{partial}{partial x}(4x) + frac{partiRead more
To apply the divergence theorem to the vector field ( mathbf{F} = 4x mathbf{i} + 7y mathbf{j} + z mathbf{k} ), we first need to calculate the divergence of ( mathbf{F} ).
The divergence ( nabla cdot mathbf{F} ) is calculated as follows:
[
nabla cdot mathbf{F} = frac{partial}{partial x}(4x) + frac{partial}{partial y}(7y) + frac{partial}{partial z}(z)
]
[
nabla cdot mathbf{F} = 4 + 7 + 1 = 12
]
Next, we need to find the volume of the cone with radius ( r = frac{1}{2pi} ) m and height ( h = 4pi^2 ) m. The volume ( V ) of a cone is given by the formula:
[
V = frac{1}{3} pi r^2 h
]
Substituting the values we have:
[
V = frac{1}{3} pi left(frac{1}{2pi}right)^2 cdot 4pi^2
]
[
= frac{1}{3} pi cdot frac{1
See lessFind the divergence theorem value for the function given by (ez , sin x, y2 )
To apply the divergence theorem, we need to find the divergence of the vector field (mathbf{F} = (e^z, sin x, y^2)).The divergence of a vector field (mathbf{F} = (F_1, F_2, F_3)) is given by the formula:[nabla cdot mathbf{F} = frac{partial F_1}{partial x} + frac{partial F_2}{partial y} + frac{partiaRead more
To apply the divergence theorem, we need to find the divergence of the vector field (mathbf{F} = (e^z, sin x, y^2)).
The divergence of a vector field (mathbf{F} = (F_1, F_2, F_3)) is given by the formula:
[
nabla cdot mathbf{F} = frac{partial F_1}{partial x} + frac{partial F_2}{partial y} + frac{partial F_3}{partial z}
]
For (mathbf{F} = (e^z, sin x, y^2)):
1. Calculate (frac{partial F_1}{partial x} = frac{partial (e^z)}{partial x} = 0)
2. Calculate (frac{partial F_2}{partial y} = frac{partial (sin x)}{partial y} = 0)
3. Calculate (frac{partial F_3}{partial z} = frac{partial (y^2)}{partial z} = 0)
Combining these results, we find:
[
nabla cdot mathbf{F} = 0 + 0 + 0 = 0
]
Since the divergence of (mathbf{F}) is (0),
See lessThe divergence theorem for a surface consisting of a sphere is computed in which coordinate system?
The divergence theorem for a surface consisting of a sphere is typically computed in spherical coordinates.
The divergence theorem for a surface consisting of a sphere is typically computed in spherical coordinates.
See lessEvaluate the surface integral ∫∫ (3x i + 2y j). dS, where S is the sphere given by x2 + y2 + z2 = 9.
To evaluate the surface integral ∫∫ (3x i + 2y j) · dS over the sphere defined by x² + y² + z² = 9, we apply the parameterization of the sphere and use the surface element.The standard approach involves using the divergence theorem, but in this case, we will directly compute the surface integral. 1.Read more
To evaluate the surface integral ∫∫ (3x i + 2y j) · dS over the sphere defined by x² + y² + z² = 9, we apply the parameterization of the sphere and use the surface element.
The standard approach involves using the divergence theorem, but in this case, we will directly compute the surface integral.
1. Recognize that the surface S is a sphere of radius 3.
2. The unit normal to the surface of the sphere is a radial vector pointing outward from the center, given by n = (x/3, y/3, z/3) on the surface of the sphere.
3. The differential area element dS on the surface of the sphere is equal to dS = R² sin(θ) dθ dφ, where R = 3.
4. The surface integral can be computed as:
∫∫_S (3x i + 2y j) · dS = ∫∫_S (3x i + 2y j) · (n dS).
5. In spherical coordinates, let:
– x = 3 sin(θ) cos(φ)
– y = 3 sin(θ) sin(φ)
– z = 3 cos(θ)
where θ ranges from 0 to π and φ ranges from 0 to 2π.
The integral
See lessGauss theorem uses which of the following operations?
Gauss's theorem, also known as Gauss's law, primarily uses the operations of integration and calculus. It relates the flux of an electric field through a closed surface to the charge enclosed within that surface. Specifically, it involves surface integrals and volume integrals.
Gauss’s theorem, also known as Gauss’s law, primarily uses the operations of integration and calculus. It relates the flux of an electric field through a closed surface to the charge enclosed within that surface. Specifically, it involves surface integrals and volume integrals.
See lessComparison of financial variables of a firm over a period of time is known as————–
Comparison of financial variables of a firm over a period of time is known as financial analysis or trend analysis.
Comparison of financial variables of a firm over a period of time is known as financial analysis or trend analysis.
See less