moving a charge from point a,where the potential is 300v, to point b,where the potential is 150v takes 4.5x 10-4 J ofwork. What is the value of the charge?
W=q•Δφ
q= W/Δφ=4.5•10⁻⁴/(300-150)= 3•10⁻⁶C
Since this motion takes energy
q= - 3•10⁻⁶C
Well, let's calculate that, but first, let's set the mood. Imagine moving a charge from point A to point B like a little electric adventure. We're going from a potential of 300 volts to 150 volts, so that's like going from the excitement of a rollercoaster to the calmness of a lazy river.
Now, the work done is given by the equation W = qΔV, where W is the work done, q is the charge, and ΔV is the change in potential. We're given that the work done is 4.5 x 10^(-4) J and the change in potential is 300 V - 150 V = 150 V.
Plugging those values into the equation, we get 4.5 x 10^(-4) J = q * 150 V. To solve for q, we divide both sides of the equation by 150 V, giving us:
q = (4.5 x 10^(-4) J) / (150 V)
Calculating that, we find:
q ≈ 3 x 10^(-6) C
So, the value of the charge is approximately 3 microCoulombs.
To find the value of the charge, we can use the equation:
\[ W = q \cdot \Delta V \]
where:
- W is the work done on the charge (given as 4.5 x 10^(-4) J)
- q is the value of the charge
- ΔV is the change in potential (ΔV = Vb - Va)
Given that the potential at point A (Va) is 300 V and at point B (Vb) is 150 V, we can substitute the values into the equation to solve for q:
\[ 4.5 \times 10^{-4} \, \text{J} = q \cdot (150 \, \text{V} - 300 \, \text{V}) \]
Simplifying the equation:
\[ 4.5 \times 10^{-4} \, \text{J} = q \cdot (-150 \, \text{V}) \]
\[ 4.5 \times 10^{-4} \, \text{J} = -150q \]
To solve for q, we divide both sides of the equation by -150:
\[ q = \frac{4.5 \times 10^{-4} \, \text{J}}{-150} \]
Calculating the value:
\[ q = -3 \times 10^{-6} \, \text{C} \]
Therefore, the value of the charge is -3 x 10^(-6) C. Note that the charge is negative, indicating that it has a negative sign (indicating an opposite charge) or that it has lost electrons during the movement.
To find the value of the charge, we can use the formula for work done in moving a charge between two points. The formula is:
Work = Charge × (Potential difference)
Given that the potential at point A is 300V and the potential at point B is 150V, and the work done is 4.5 × 10^(-4) J, we can substitute these values into the formula.
4.5 × 10^(-4) J = Charge × (300V - 150V)
Simplifying:
4.5 × 10^(-4) J = Charge × 150V
Now we can solve for the value of the charge. Dividing both sides of the equation by 150V:
Charge = (4.5 × 10^(-4) J) / 150V
Calculating on a calculator:
Charge = 3 × 10^(-6) C
Therefore, the value of the charge is 3 × 10^(-6) Coulombs.