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Mashcka [7]
3 years ago
15

Three individual point charges are placed at the following positions in the x-y plane:Q3= 5.0 nC at (x, y) = (0,0);Q2= -3.0 nC a

t (x, y) = (4 cm, 0); and Q1= ?nC at (x, y) = (2 cm,0);What isthe magnitude, and sign, ofcharge Q1such that the net force exerted on charge Q3, exerted bycharges Q1and Q2, is zero?
Physics
1 answer:
ozzi3 years ago
8 0

Answer:

Explanation:

net force exerted on charge Q₃, exerted by charges Q₁and Q₂, will be  zero

if net  electric field due to charges Q₁ and Q₂  at origin is zero .

electric field due to Q₂

= 9 X 10⁹ X 3 x10⁹ / .04²

electric field due to Q₁

= 9 X 10⁹ X Q₁ / .02²

For equilibrium

9 X 10⁹ X Q₁ / .02² = 9 X 10⁹ X 3 x10⁻⁹ / .04²

Q₁  = 3 X10⁻⁹ x .02² / .04²

= 3 / 4 x 10⁻⁹

.75 x 10⁻⁹  C

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Answer:

(a). The magnitude of the net force is (2.1\times10^{-18}\ N)k

(b). The magnitude of the net force is (4.23\times10^{-19}\ N)k

(c). The magnitude of the net force is (8.4\times10^{-19}\ N)i+(12.6\times10^{-19}\ N)k

Explanation:

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F=F_{e}+F_{B}

(a). If the electric field is in the positive z direction and has a magnitude of 5.25 V/m,

We need to calculate the magnitude of the net force acting on the proton

Using formula of net force

F_{net}=e(E+v\times B)

Put the value into the formula

F_{net}=1.6\times10^{-19}(5.25k+2230\times-3.54\times10^{-3}(j\times i))

F_{net}=1.6\times10^{-19}(5.25k+2230\times-3.54\times10^{-3}(-k))

F_{net}=(2.1\times10^{-18}\ N)k

(b). If the electric field is in the negative z direction and has a magnitude of 5.25 V/m,

We need to calculate the magnitude of the net force acting on the proton

Using formula of net force

F_{net}=e(E+v\times B)

Put the value into the formula

F_{net}=1.6\times10^{-19}(-5.25k+2230\times-3.54\times10^{-3}(j\times i))

F_{net}=1.6\times10^{-19}(-5.25k+2230\times-3.54\times10^{-3}(-k))

F_{net}=(4.23\times10^{-19}\ N)k

(c). If the electric field is in the positive x direction and has a magnitude of 5.25 V/m

We need to calculate the magnitude of the net force acting on the proton

Using formula of net force

F_{net}=e(E+v\times B)

Put the value into the formula

F_{net}=1.6\times10^{-19}(5.25i+2230\times-3.54\times10^{-3}(j\times i))

F_{net}=(8.4\times10^{-19}\ N)i+(12.6\times10^{-19}\ N)k

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(b). The magnitude of the net force is (4.23\times10^{-19}\ N)k

(c). The magnitude of the net force is (8.4\times10^{-19}\ N)i+(12.6\times10^{-19}\ N)k

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