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Evaluate Gauss law for D = 5r2 /4 i in spherical coordinates with r = 4m and θ = π/2
c Explanation: ∫∫ ( 5r2 /4) . (r2 sin θ dθ dφ), which is the integral to be evaluated. Put r = 4m and substitute θ = 0→ π/4 and φ = 0→ 2π, the integral evaluates to 588.9
c
See lessExplanation: ∫∫ ( 5r2
/4) . (r2 sin θ dθ dφ), which is the integral to be evaluated.
Put r = 4m and substitute θ = 0→ π/4 and φ = 0→ 2π, the integral evaluates to 588.9
A field in which a test charge around any closed surface in static path is zero is called
d Explanation: Work done in moving a charge in a closed path is zero. It is expressed as, ∫ E.dl = 0. The field having this property is called conservative or lamellar field.
d
See lessExplanation: Work done in moving a charge in a closed path is zero. It is expressed as, ∫
E.dl = 0. The field having this property is called conservative or lamellar field.
dentify the nature of the field, if the divergence is zero and curl is also zero
c Explanation: Since the vector field does not diverge (moves in a straight path), the divergence is zero. Also, the path does not possess any curls, so the field is irrotational.
c
See lessExplanation: Since the vector field does not diverge (moves in a straight path), the
divergence is zero. Also, the path does not possess any curls, so the field is irrotational.
Given B= (10/r)i+( rcos θ) j+k in spherical coordinates. Find Cartesian points at (-3,4,0)
a Explanation: r = √(x2+y2+z2 ) = √25 = 5 Θ = cos-1 (z/r) = 1 Φ = tan-1 (y/x) = tan-1 (-4/3) Thus, B = -2i + j.
a
See lessExplanation: r = √(x2+y2+z2
) = √25 = 5
Θ = cos-1
(z/r) = 1
Φ = tan-1
(y/x) = tan-1
(-4/3)
Thus, B = -2i + j.
A charge located at point p (5,30⁰,2) is said to be in which coordinate system?
b Explanation: The cylindrical system is of the form (ρ, φ, z), which relates the point given in the question
b
See lessExplanation: The cylindrical system is of the form (ρ, φ, z), which relates the point given
in the question
Vector transformation followed by coordinate point substitution and viceversa, both given the same result. Choose the best answer
a Explanation: The order of vector transformation and point substitution will not affect the result, only when the vector is a constant
a
See lessExplanation: The order of vector transformation and point substitution will not affect the
result, only when the vector is a constant
Find the potential between two points p(1,-1,0) and q(2,1,3) with E = 40xy i + 20×2 j + 2 k
c Explanation: V = -∫ E.dl = -∫ (40xy dx + 20x2 dy + 2 dz) , from q to p. On integrating, we get 106 volts.
c
See lessExplanation: V = -∫ E.dl = -∫ (40xy dx + 20×2 dy + 2 dz) , from q to p.
On integrating, we get 106 volts.
An electric field is given as E = 6y2z i + 12xyz j + 6xy2 k. An incremental path is given by dl = -3 i + 5 j – 2 k mm. The work done in moving a 2mC charge along the path if the location of the path is at p(0,2,5) is (in Joule)
b Explanation: W = -Q E.dl W = -2 X 10-3 X (6y2z i + 12xyz j + 6xy2 k) . (-3 i + 5 j -2 k) At p(0,2,5), W = -2(-18.22.5) X 10-3 = 0.72 J.
b
See lessExplanation: W = -Q E.dl
W = -2 X 10-3 X (6y2z i + 12xyz j + 6xy2 k) . (-3 i + 5 j -2 k)
At p(0,2,5), W = -2(-18.22.5) X 10-3 = 0.72 J.
Convert the given rectangular coordinates A(2,3,1) into corresponding cylindrical coordinates
d Explanation: ρ = √(x2+y2 ) = √13 = 3.61 Φ = tan-1 (y/x) = 56.31 z = 1 Thus, A = (3.61,56.31,1).
d
See lessExplanation: ρ = √(x2+y2
) = √13 = 3.61
Φ = tan-1
(y/x) = 56.31
z = 1
Thus, A = (3.61,56.31,1).
What is the value of the alternative core lengths below which variation in rating can be obtained?
d Explanation: The variation in the ratings can be obtained using alternative core lengths. The value of the alternative core lengths below 0.5 * length or 0.7 * length provides the variation in the ratings
d
See lessExplanation: The variation in the ratings can be obtained using alternative core lengths.
The value of the alternative core lengths below 0.5 * length or 0.7 * length provides the
variation in the ratings