Three negative point charges lie along a line as shown in Fig. E21.41 . Find the magnitude and direction of the electric field this combination of charges produces at point P , which lies 6.00 cm from the −2.00 μ C charge measured perpendicular to the line connecting the three charges. 21.41. IDENTIFY: E = k | q | r 2 . The net field is the vector sum of the fields due to each charge. SET UP: The electric field of a negative charge is directed toward the charge. Label the charges q 1 , q 2 , and q 3 , as shown in Figure 21.41a. This figure also shows additional distances and angles. The electric fields at point P are shown in Figure 21.41b. This figure also shows the xy -coordinates we will use and the x - and y -components of the fields E → 1 , E → 2 , and E → 3 . EXECUTE: E 1 = E 3 = ( 8.99 × 10 9 N · m 2 / C 2 ) 5.00 × 10 − 6 C ( 0.100 m ) 2 = 4.49 × 10 6 N / C . E 2 = ( 8.99 × 10 9 N · m 2 / C 2 ) 2.00 × 10 − 6 C ( 0.0600 m ) 2 = 4.99 × 10 6 N / C E y = E 1 y + E 2y + E 3 y = 0 and E x = E 1 x + E 2 x + E 3 x = E 2 + 2 E 1 cos53.1° = 1.04 × 10 7 N/C. E = 1.04 × 10 7 N/C, toward the −2.00 μ C charge. EVALUATE: The x -components of the fields of all three charges are in the same direction. Figure 21.41
Three negative point charges lie along a line as shown in Fig. E21.41 . Find the magnitude and direction of the electric field this combination of charges produces at point P , which lies 6.00 cm from the −2.00 μ C charge measured perpendicular to the line connecting the three charges. 21.41. IDENTIFY: E = k | q | r 2 . The net field is the vector sum of the fields due to each charge. SET UP: The electric field of a negative charge is directed toward the charge. Label the charges q 1 , q 2 , and q 3 , as shown in Figure 21.41a. This figure also shows additional distances and angles. The electric fields at point P are shown in Figure 21.41b. This figure also shows the xy -coordinates we will use and the x - and y -components of the fields E → 1 , E → 2 , and E → 3 . EXECUTE: E 1 = E 3 = ( 8.99 × 10 9 N · m 2 / C 2 ) 5.00 × 10 − 6 C ( 0.100 m ) 2 = 4.49 × 10 6 N / C . E 2 = ( 8.99 × 10 9 N · m 2 / C 2 ) 2.00 × 10 − 6 C ( 0.0600 m ) 2 = 4.99 × 10 6 N / C E y = E 1 y + E 2y + E 3 y = 0 and E x = E 1 x + E 2 x + E 3 x = E 2 + 2 E 1 cos53.1° = 1.04 × 10 7 N/C. E = 1.04 × 10 7 N/C, toward the −2.00 μ C charge. EVALUATE: The x -components of the fields of all three charges are in the same direction. Figure 21.41
Three negative point charges lie along a line as shown in Fig. E21.41. Find the magnitude and direction of the electric field this combination of charges produces at point P, which lies 6.00 cm from the −2.00 μC charge measured perpendicular to the line connecting the three charges.
21.41. IDENTIFY:
E
=
k
|
q
|
r
2
. The net field is the vector sum of the fields due to each charge.
SET UP: The electric field of a negative charge is directed toward the charge. Label the charges q1, q2, and q3, as shown in Figure 21.41a. This figure also shows additional distances and angles. The electric fields at point P are shown in Figure 21.41b. This figure also shows the xy-coordinates we will use and the x- and y-components of the fields
E
→
1
,
E
→
2
, and
E
→
3
.
EXECUTE:
E
1
=
E
3
=
(
8.99
×
10
9
N
·
m
2
/
C
2
)
5.00
×
10
−
6
C
(
0.100
m
)
2
=
4.49
×
10
6
N
/
C
.
E
2
=
(
8.99
×
10
9
N
·
m
2
/
C
2
)
2.00
×
10
−
6
C
(
0.0600
m
)
2
=
4.99
×
10
6
N
/
C
Ey = E1y + E2y + E3y = 0 and Ex = E1x + E2x + E3x = E2 + 2E1cos53.1° = 1.04 × 107 N/C.
E = 1.04 × 107 N/C, toward the −2.00 μC charge.
EVALUATE: The x-components of the fields of all three charges are in the same direction.
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