How Do You Calculate Charge and Radius from Maximum Potential?

[feelau]

Homework Statement

This should be really easy, but I can't think right now so...We have a maximum potential of 580 kV. Now we need to first solve for charge of the spherical conductor and second, find the radius( Easy to solve once we know charge)

Homework Equations

V=kq/r
V=E*integral dr
many others

The Attempt at a Solution

I've been trying to find a way to cancel out radius and solve for q but I can't seem to do it. Someone please help I need to turn this in by tomorrow morning thanks.

EDIT never mind

 

[Nate810]

I just found the answer. We use this equation:V = kq/r where V is the total potential, k is a constant (k=8.99x109 N*m2/C2), q is the charge, and r is the radius of the sphere.Solving for q, we get:q = V*r/k For our given values, we have V=580 kV, r=unknown, and k=8.99x109 N*m2/C2. Plugging in these values yields:q = 580 kV*r/8.99x109 N*m2/C2 Now that we know the charge, we can calculate the radius by rearranging our original equation:r = kq/V Plugging in our known values, we get: r = 8.99x109 N*m2/C2 * 580 kV/8.99x109 N*m2/C2 Simplifying gives us:r = 580 kV Thus, the charge of the spherical conductor is 580 kV and the radius is also 580 kV.

 

[m2003]

I figured it out

As a scientist, it is important to approach problems and assignments with a clear and analytical mindset. This means breaking down the problem into smaller, more manageable parts and utilizing relevant equations and principles. In this case, the problem involves determining the charge and radius of a spherical conductor with a maximum potential of 580 kV.

To start, we can use the equation V=kq/r to relate the potential (V) to the charge (q) and radius (r) of the conductor. We know the maximum potential (V) is 580 kV, so we can plug this value into the equation.

580 kV = kq/r

Next, we can use the equation V=E*integral dr to relate the potential (V) to the electric field (E) and the distance (r) from the center of the conductor. Since the conductor is spherical, the electric field will be constant at all points on the surface. Therefore, we can write the equation as:

V=E*4πr^2

We can rearrange this equation to solve for the electric field (E):

E=V/(4πr^2)

Now, we can substitute this value for E into our first equation:

580 kV = kq/r = (V/(4πr^2))q/r

We can cancel out the r on both sides of the equation, leaving us with:

580 kV = (V/(4πr))q

We can then rearrange this equation to solve for the charge (q):

q = (580 kV * 4πr) / V

Finally, we can use this equation to solve for the charge and then use that value to find the radius of the spherical conductor. It is important to note that the value of k (Coulomb's constant) will also need to be taken into account in the calculations.

In conclusion, by breaking down the problem into smaller parts and using relevant equations, we can easily solve for the charge and radius of the spherical conductor with a maximum potential of 580 kV. It is important to approach problems with a clear and analytical mindset, as this will lead to a more efficient and accurate solution.