We read your photo as:

Calculate the electrostatic force between two spheres with charges q1 = 2 x 10⁻⁷ C and q2 = 3 x 10⁻⁷ C, separated by 30 cm.

Physics

ScanSolve AI Answer

Step-by-step solution

5 steps
  1. Identify the given values for Question 5.

    The charges on the spheres are q1=2×10−7 Cq_1 = 2 \times 10^{-7} \text{ C} and q2=3×10−7 Cq_2 = 3 \times 10^{-7} \text{ C}.
    The distance between the spheres is r=30 cm=0.30 mr = 30 \text{ cm} = 0.30 \text{ m}.
    The electrostatic constant for air is k=14πϵ0=9×109 N m2/C2k = \frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \text{ N m}^2/\text{C}^2.

  2. Calculate the electrostatic force using Coulomb's Law.

    The formula for Coulomb's Law is F=kq1q2r2F = k \frac{q_1 q_2}{r^2}.

    F=(9×109 N m2/C2)(2×10−7 C)×(3×10−7 C)(0.30 m)2F = (9 \times 10^9 \text{ N m}^2/\text{C}^2) \frac{(2 \times 10^{-7} \text{ C}) \times (3 \times 10^{-7} \text{ C})}{(0.30 \text{ m})^2} F=(9×109)6×10−140.09 NF = (9 \times 10^9) \frac{6 \times 10^{-14}}{0.09} \text{ N} F=(9×109)×(66.66...×10−14) NF = (9 \times 10^9) \times (66.66... \times 10^{-14}) \text{ N} F=600×10−5 NF = 600 \times 10^{-5} \text{ N} F=6×10−3 NF = 6 \times 10^{-3} \text{ N}

    Since both charges are positive, the force is repulsive.
    The force is 6×10−3 N\boxed{\mathbf{6 \times 10^{-3} \text{ N}}} and is repulsive.

  3. Identify the given values for Question 6 (a).

    The charge on the first sphere is q1=0.4μC=0.4×10−6 Cq_1 = 0.4 \mu\text{C} = 0.4 \times 10^{-6} \text{ C}.
    The force experienced is F=0.2 NF = 0.2 \text{ N}.
    The charge on the second sphere is q2=0.8μC=0.8×10−6 Cq_2 = 0.8 \mu\text{C} = 0.8 \times 10^{-6} \text{ C}.
    The electrostatic constant for air is k=9×109 N m2/C2k = 9 \times 10^9 \text{ N m}^2/\text{C}^2.

  4. Calculate the distance between the spheres for Question 6 (a).

    Using Coulomb's Law, F=kq1q2r2F = k \frac{q_1 q_2}{r^2}. We need to find rr.
    Rearranging the formula for r2r^2:

    r2=kq1q2Fr^2 = k \frac{q_1 q_2}{F}

    Substitute the given values:

    r2=(9×109 N m2/C2)(0.4×10−6 C)×(0.8×10−6 C)0.2 Nr^2 = (9 \times 10^9 \text{ N m}^2/\text{C}^2) \frac{(0.4 \times 10^{-6} \text{ C}) \times (0.8 \times 10^{-6} \text{ C})}{0.2 \text{ N}} r2=(9×109)0.32×10−120.2 m2r^2 = (9 \times 10^9) \frac{0.32 \times 10^{-12}}{0.2} \text{ m}^2 r2=(9×109)×(1.6×10−12) m2r^2 = (9 \times 10^9) \times (1.6 \times 10^{-12}) \text{ m}^2 r2=14.4×10−3 m2r^2 = 14.4 \times 10^{-3} \text{ m}^2 r2=0.0144 m2r^2 = 0.0144 \text{ m}^2

    Now, take the square root to find rr:

    r=0.0144 m2r = \sqrt{0.0144 \text{ m}^2} r=0.12 mr = 0.12 \text{ m}

    Converting to centimeters:

    r=0.12×100 cm=12 cmr = 0.12 \times 100 \text{ cm} = 12 \text{ cm}

    The distance between the spheres is 0.12 m or 12 cm\boxed{\mathbf{0.12 \text{ m} \text{ or } 12 \text{ cm}}}.

  5. Determine the force on the second sphere due to the first for Question 6 (b).

    According to Newton's third law, the force exerted by the first sphere on the second sphere is equal in magnitude and opposite in direction to the force exerted by the second sphere on the first sphere.
    Therefore, if the first sphere experiences a force of 0.2 N0.2 \text{ N} due to the second sphere, the second sphere will also experience a force of 0.2 N0.2 \text{ N} due to the first sphere.
    The force on the second sphere due to the first sphere is 0.2 N\boxed{\mathbf{0.2 \text{ N}}}.

Was this helpful?

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp