)Two like charges of 20µC are placed 5cm apart in a medium of dielectric constant 2.5. Calculate the force between them.
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Two charges +5μC and +10μC are placed 20 cm apart. The electric field at the midpoint between the two charges is:
Hard
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Correct option is
C
13.5×10
6
N/C towards +5μC
Let the two charges placed at two points of line AB as A and B whose distance is 20 cm and O is the mid point of the line AB
Distance between the two charges , AB=20 cm
∴AO=OB
Net elctric at O=E
Electric field at point O caused by +5\mu C charge,
E
1
=
4πε
0
(AO)
2
5×10
−6
=
4πε
0
(10×10
−2
)
2
5×10
−6
N/C toward +5μC
where,
ε
0
=Permittivity of free space
4πε
1
=9×10
9
Nm
2
C
−2
Magnitude of electric field at point O cause by +10\mu C charge,
E
1
=
4πε
0
(AO)
2
10×10
−6
=
4πε
0
(10×10
−2
)
2
10×10
−6
N/C towards +10μC
∴E=E
1
+E
2
=
(10×10
−2
)
2
9×10
9
×15×10
−6
=13.5×10
6
N/C towards +5μC