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If a potential V is 2V at x = 1mm and is zero at x=0 and volume charge density is -106εo, constant throughout the free space region between x = 0 and x = 1mm. Calculate V at x = 0.5mm.
Answer: d Explanation: Del2 (V) = -ρv/εo= +106 On integrating twice with respect to x, V = 106. (x2 /2) + C1x + C2. Substitute the boundary conditions, x = 0, V = 0 and x = 1mm, V = 2V in V, C1 = 1500 and C2 = 0. At x = 0.5mm, we get, V = 0.875V.
Answer: d
Explanation: Del2
(V) = -ρv/εo= +106
On integrating twice with respect to x, V = 106. (x2
/2) + C1x + C2.
Substitute the boundary conditions, x = 0, V = 0 and x = 1mm, V = 2V in V,
C1 = 1500 and C2 = 0. At x = 0.5mm, we get, V = 0.875V.
See lessThe divergence theorem converts
Answer: b Explanation: The divergence theorem is given by, ∫∫ D.ds = ∫∫∫ Div (D) dv. It is clear that it converts surface (double) integral to volume(triple) integral.
Answer: b
Explanation: The divergence theorem is given by, ∫∫ D.ds = ∫∫∫ Div (D) dv. It is clear that it
converts surface (double) integral to volume(triple) integral.
See lessEvaluate Gauss law for D = 5r2 /4 i in spherical coordinates with r = 4m and θ = π/2 as volume integral.
Answer: b Explanation: ∫∫ D.ds = ∫∫∫ Div (D) dv, where RHS needs to be computed. The divergence of D given is, Div(D) = 5r and dv = r2 sin θ dr dθ dφ. On integrating, r = 0->4, φ = 0->2π and θ = 0->π/4, we get Q = 588.9.
Answer: b
Explanation: ∫∫ D.ds = ∫∫∫ Div (D) dv, where RHS needs to be computed.
The divergence of D given is, Div(D) = 5r and dv = r2 sin θ dr dθ dφ. On integrating, r =
0->4, φ = 0->2π and θ = 0->π/4, we get Q = 588.9.
See lessA field in which a test charge around any closed surface in static path is zero is called
Answer: 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.
Answer: 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.
See lessThe potential in a lamellar field is
Answer: b Explanation: Work done in a lamellar field is zero. ∫ E.dl = 0,thus ∑V = 0. The potential will be zero.
Answer: b
Explanation: Work done in a lamellar field is zero. ∫ E.dl = 0,thus ∑V = 0. The potential
will be zero.
See lessLine integral is used to calculate
Answer: d Explanation: Length is a linear quantity, whereas area is two dimensional and volume is three dimensional. Thus single or line integral can be used to find length in general.
Answer: d
Explanation: Length is a linear quantity, whereas area is two dimensional and volume is
three dimensional. Thus single or line integral can be used to find length in general.
See lessSurface integral is used to compute
Answer: b Explanation: Surface integral is used to compute area, which is the product of two quantities length and breadth. Thus it is two dimensional integral.
Answer: b
Explanation: Surface integral is used to compute area, which is the product of two
quantities length and breadth. Thus it is two dimensional integral.
See lessEvaluate Gauss law for D = 5r2 /4 i in spherical coordinates with r = 4m and θ = π/2.
Answer: 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.
Answer: 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.
See lessCurl cannot be empl oyed in which one of the following?
Answer: d Explanation: In the Directional coupler, Magic Tee, Isolator and Terminator the EM waves travel both in linear and angular motion, which involves curl too. But in waveguides, as the name suggests, only guided propagation occurs (no bending or curl of waves)
Answer: d
Explanation: In the Directional coupler, Magic Tee, Isolator and Terminator the EM
waves travel both in linear and angular motion, which involves curl too. But in
waveguides, as the name suggests, only guided propagation occurs (no bending or curl
of waves)
See lessWhich of the following Maxwell equations use curl operation?
Answer: a Explanation: Maxwell 1st equation, Curl (H) = J (Ampere law) Maxwell 2nd equation, Curl (E) = -D(B)/Dt (Faraday’s law) Maxwell 3rd equation, Div (D) = Q (Gauss law for electric field) Maxwell 4th equation, Div (B) = 0(Gauss law for magnetic field) It is clear that only 1st and 2nd equationRead more
Answer: a
Explanation: Maxwell 1st equation, Curl (H) = J (Ampere law)
Maxwell 2nd equation, Curl (E) = -D(B)/Dt (Faraday’s law)
Maxwell 3rd equation, Div (D) = Q (Gauss law for electric field)
Maxwell 4th equation, Div (B) = 0(Gauss law for magnetic field)
It is clear that only 1st and 2nd equations use the curl operation.
See less