The charge of the point charge will be "-2.94 μC".
Given values:
- Electric field, [tex]E = 750 \ kN/C \ or \ 750\times 10^3[/tex]
- Radius, [tex]r = 15 \ cm \ or \ 0.15 \ m[/tex]
- Charge, [tex]4.8 \ \mu C[/tex]
By using Gauss law,
→ [tex]EA = \frac{q_{enc}}{\varepsilon_0}[/tex]
or,
→ [tex]E(4 \pi r^2) = \frac{q_{enc}}{\varepsilon_0}[/tex]
Now,
The amount of charge enclosed,
→ [tex]q_{enc} = 4 \pi \varepsilon_0 r^2 E[/tex]
By substituting the values,
[tex]= 4\pi (8.85\times 10^{-12})(0.15)^2(750\times 10^3)[/tex]
[tex]= 1.88\times 10^{-6} \ C[/tex]
[tex]= 1.88 \ \mu C[/tex]
hence,
On point charge, the charge will be:
→ [tex]q = 1.88-4.8[/tex]
[tex]= -2.92 \ \mu C[/tex]
Thus the above answer is right.
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