Solved Exercise/Numericals - Electric Field Intensity (E) & Force (F) - 1.


Q.1 Point charges Q1 = 5 μC and Q2 = -4 μC are placed at (3, 2, 1) and (-4, 0, 6) respectively. Determine the force on Q1.
Ans:
Force on Q1 due to Q2 is given as :












= -5.74 ax – 1.642 ay + 4.104 az mN



Q. 2 Five Identical 15 μC point charges are located at the center and corners of a square defined by -1 < x, y > 1 and z = 0.
Find the force on the 10 μC point charge at (0, 0, 2).












Therefore,
F / 1.35 = [(0, 0, 2) / 8] + [(-1, -1, 2) / 63/2] + [(1, -1, 2) / 63/2]
             + [(-1, 1, 2) / 63/2] + [(1, 1, 2) / 63/2]

→ F = 1.35 [(0.25 + (8 / 63/2)] az

        = 1.072az N



Q.3 Point Charges Q1 and Q2 are respectively located at (4, 0, -3) and (2, 0, 1). If Q2 = 4nC, find Q1 such that
a) The E at (5, 0, 6) has no z component.
b) The force on a test charge at (5, 0, 6) has no x component.

a) Electric field intensity at point (5, 0, 6) is given as:
















Hence Q1 = - 3.463 nC.

b) F (5, 0, 6) = qE (5, 0, 6)

If Ex = 0













Hence, Q1 = -18.7 nC.



Q. 4 Determine the total charge
a) On line 0 < x < 5 m if ρL = 2x2 mC/m
Ans:

Q = ∫L ρl dl

= ∫05 (2 x2)dx

= | 4x3 |05 = 0.5 C

b) On the cylinder ρ = 3, 0 < z < 4, if ρs = ρz2 nC/m2∫S ρsds = ∫S ρz2 ds

= ∫S  ρz2 (ρ dφ dz)

= ∫(φ =0)2π ∫(z =0)4  ρz2 (ρ dφ dz)

= (ρ3 / 3) (2π) | z3 / 3 |04

= 9 x (2π) x (43 / 3)

= 1.206 μC

c) Within the sphere r = 4m, if ρv = 10 / (r sinθ ) C / m3
Ans:
Q = ∫V ρvdv

= ∫V [ 10 / (r sinθ ) ]  (r2 sinθ dr dθ dφ)

= ∫(r=0)4  ∫(θ=0)π  ∫(φ=0)2π  (10 rdr dθ dφ)

= 10 | r2 / 2 |04 (2π) (π)

= 157.91 C



ALSO READ:

- Introduction To Electrostatics.

- Coulomb's law.

- Electric Field Intensity (E).

- Electric Lines Of Forces /Streamlines / Electric Flux (ψ) .

- Electric Flux Density (D).

- Electric Field Intensity Due To a Finite and Infinite Line Charge.

- Electric Field Intensity Due To a Infinite Sheet Charge.

- Electric Field Intensity Due To a Circular Ring Charge.

- Electric Field Intensity Due To a Circular Disk Charge.

- Numericals / Solved Examples - Electric Force and Field Intensity.

- Numericals / Solved Examples - Electric Field Intensity - Line, Surface and Mixed Charge Configuration.

- Short Notes/FAQ's

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