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If the radius of a sphere is 1/(4π)m and the electric flux density is 16π units, the total flux is given by
c Explanation: Total flux leaving the entire surface is, ψ = 4πr2D from Gauss law. Ψ = 4π(1/16π2 ) X 16π = 4.
c
See lessExplanation: Total flux leaving the entire surface is, ψ = 4πr2D from Gauss law. Ψ =
4π(1/16π2
) X 16π = 4.
Find the flux density of line charge of radius (cylinder is the Gaussian surface) 2m and charge density is 3.14 units?
d Explanation: The electric field of a line charge is given by, E = λ/(2περ), where ρ is the radius of cylinder, which is the Gaussian surface and λ is the charge density. The density D = εE = λ/(2πρ) = 3.14/(2π X 2) = 1/4 = 0.25.
d
See lessExplanation: The electric field of a line charge is given by, E = λ/(2περ), where ρ is the
radius of cylinder, which is the Gaussian surface and λ is the charge density. The
density D = εE = λ/(2πρ) = 3.14/(2π X 2) = 1/4 = 0.25.
A uniform surface charge of σ = 2 μC/m2 , is situated at z = 2 plane. What is the value of flux density at P(1,1,1)m?
b Explanation: The flux density of any field is independent of the position (point). D = σ/2 = 2 X 10-6 (-az)/2 = -10
b
See lessExplanation: The flux density of any field is independent of the position (point). D = σ/2 =
2 X 10-6
(-az)/2 = -10
A charge of 2 X 10-7 C is acted upon by a force of 0.1N. Determine the distance to the other charge of 4.5 X 10-7 C, both the charges are in vacuum
d Explanation: F = q1q2/(4∏εor2 ) , substituting q1, q2 and F, r2 = q1q2/(4∏εoF) = We get r = 0.09m
d
See lessExplanation: F = q1q2/(4∏εor2
) , substituting q1, q2 and F, r2 = q1q2/(4∏εoF) =
We get r = 0.09m
Two small diameter 10gm dielectric balls can slide freely on a vertical channel. Each carry a negative charge of 1μC. Find the separation between the balls if the lower ball is restrained from moving
c Explanation: F = mg = 10 X 10-3 X 9.81 = 9.81 X 10-2 N. On calculating r by substituting charges, we get r = 0.3m
c
See lessExplanation: F = mg = 10 X 10-3 X 9.81 = 9.81 X 10-2 N.
On calculating r by substituting charges, we get r = 0.3m
Find the force between two charges when they are brought in contact and separated by 4cm apart, charges are 2nC and -1nC, in μN
c Explanation: Before the charges are brought into contact, F = 11.234 μN. After charges are brought into contact and then separated, charge on each sphere is, (q1 + q2)/2 = 0.5nC On calculating the force with q1 = q2 = 0.5nC, F = 1.404μN
c
See lessExplanation: Before the charges are brought into contact, F = 11.234 μN.
After charges are brought into contact and then separated, charge on each sphere is,
(q1 + q2)/2 = 0.5nC
On calculating the force with q1 = q2 = 0.5nC, F = 1.404μN
Find the force of interaction between 60 stat coulomb and 37.5 stat coulomb spaced 7.5cm apart in transformer oil(εr=2.2) in 10-4 N
d Explanation: 1 stat coulomb = 1/(3 X 109 ) C F = (1.998 X 1.2488 X 10-16)/(4∏ X 8.854 X 10-12 X 2.2 X (7.5 X 10-2 ) 2 ) = 1.815 X 10-4 N
d
See lessExplanation: 1 stat coulomb = 1/(3 X 109
) C
F = (1.998 X 1.2488 X 10-16)/(4∏ X 8.854 X 10-12 X 2.2 X (7.5 X 10-2
)
2
) = 1.815 X 10-4 N
Two charges 1C and -4C exists in air. What is the direction of force?
c Explanation: Since the charges are unlike, the force will be attractive. Thus the force directs from 1C to -4C
c
See lessExplanation: Since the charges are unlike, the force will be attractive. Thus the force
directs from 1C to -4C
Find the force between 2C and -1C separated by a distance 1m in air(in newton).
b Explanation: F = q1q2/(4∏εor2 ) = -2 X 9/(10-9 X 12) = -18 X 10
b
See lessExplanation: F = q1q2/(4∏εor2
) = -2 X 9/(10-9 X 12) = -18 X 10
For 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.
b Explanation: Div (F) = 4 + 7 + 1 = 12. The divergence theorem gives ∫∫∫(12).dV, where dV is the volume of the cone πr3h/3, where r = 1/2π m and h = 4π2 m. On substituting the radius and height in the triple integral, we get 2 units.
b
See lessExplanation: Div (F) = 4 + 7 + 1 = 12. The divergence theorem gives ∫∫∫(12).dV, where
dV is the volume of the cone πr3h/3, where r = 1/2π m and h = 4π2 m. On substituting the
radius and height in the triple integral, we get 2 units.