Answer:
0.388
Step-by-step explanation:
To find the distance to the charged object producing the given electric field, we can use Coulomb's law, which relates the electric field strength (E) to the charge (Q) and distance (r) between the charged object and the point where the electric field is measured:
�
=
�
⋅
∣
�
∣
�
2
E=
r
2
k⋅∣Q∣
where:
�
E is the electric field strength (given as 2.75x10^5 N/C).
�
k is Coulomb's constant, approximately equal to 8.99x10^9 N m^2/C^2.
∣
�
∣
∣Q∣ is the magnitude of the charge (given as 4.60x10^-6 C).
�
r is the distance between the charged object and the point where the electric field is measured (to be found).
Now, let's rearrange the equation to solve for
�
r:
�
=
�
⋅
∣
�
∣
�
r=
E
k⋅∣Q∣
Substitute the given values:
�
=
(
8.99
×
1
0
9
N m
2
/
C
2
)
⋅
(
4.60
×
1
0
−
6
C
)
2.75
×
1
0
5
N/C
r=
2.75×10
5
N/C
(8.99×10
9
N m
2
/C
2
)⋅(4.60×10
−6
C)
�
=
8.99
×
1
0
9
×
4.60
×
1
0
−
6
2.75
×
1
0
5
r=
2.75×10
5
8.99×10
9
×4.60×10
−6
�
=
41.434
×
1
0
3
2.75
×
1
0
5
r=
2.75×10
5
41.434×10
3
�
=
0.15087
r=
0.15087
�
≈
0.388
meters
r≈0.388meters
The distance to the charged object producing the electric field is approximately 0.388 meters.