Question

In: Physics

A 5.4-µC point charge is located at x = 1.1 m, y = 2.9 m, and...

A 5.4-µC point charge is located at x = 1.1 m, y = 2.9 m, and a -4.3-µC point charge is located at x = 2.3 m, y = -1.9 m.

(a) Find the magnitude and direction of the electric field at x = -2.7 m, y = 1.2 m.

magnitude kN/C
direction °


(b) Find the magnitude and direction of the force on a proton at x = -2.7 m, y = 1.2 m.

magnitude N
direction °

Solutions

Expert Solution

a)

q1 = 5.4 x 10-6 C

r1 = 1.1 i + 2.9 j

q2 = - 4.3 x 10-6 C

r2 = 2.3 i - 1.9 j

r3 = - 2.7 i + 1.2 j

r31 = r3 - r1 = (- 2.7 i + 1.2 j ) - (1.1 i + 2.9 j ) = - 3.8 i - 1.7 j

|r31| = sqrt((- 3.8 )2 + (- 1.7)2) = 4.2 m

r23 = r2 - r3 = 2.3 i - 1.9 j - (- 2.7 i + 1.2 j ) = 5 i - 3.1 j

|r23| = sqrt((5 )2 + (- 3.1)2) = 5.9 m

E1 = electric field by charge q1 = k q1 r31 /(|r31| )2 = (9 x 109) (5.4 x 10-6) (- 3.8 i - 1.7 j)/(4.2)2

E1 = 2755.1 (- 3.8 i - 1.7 j) = - (1.05 x 104) i - (4.7 x 103) j

E2 = electric field by charge q2 = k q2 r23 /(|r23| )2 = (9 x 109) (4.3 x 10-6) (5 i - 3.1 j )/(5.9)2

E2 = (1111.75) (5 i - 3.1 j) = (5.6 x 103) i - (3.5 x 103) j

Net e;lectric field is given as

E = E1 + E2

E = - (1.05 x 104) i - (4.7 x 103) j + (5.6 x 103) i - (3.5 x 103) j

E = - 4900 i - 8200 j

magnitude : sqrt((- 4900)2 + (- 8200)2) = 9.6 x 103 N/C

direction : 180 + tan-1(8200/4900) = 239.13 deg counterclockwise from +X-axis

b)

q = charge on proton = 1.6 x 10-19 C

force on proton is given as

F = q E

F = (1.6 x 10-19) (9.6 x 103)

F = (15.36 x 10-16) N

direction :239.13 deg counterclockwise from +X-axis


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