point charges +1 micro coulomb and +4 microcoulomb are separated by a distance 4cm in air what is the distance of a null point from the small charge? what is the electric potential at null point?
the electric oppose, and where they are equal and opposite... x is the distance from the smaller charge
k/(x^2)=k4/(x-.04)^2
4x^2=x^2-.08x+.04^2
3x^2+.08x-.0016=0
x=(-.08+-sqrt(.0064+12*.0015))/6
x= 0.0127m=1.27cm from smaller charge
potential=k(1/1.27+4/(4-1.27))
To find the distance of the null point from the small charge, we can use the concept of electric field due to point charges. The distance of the null point from the small charge can be obtained by equating the electric field contributions from both charges.
The electric field due to a point charge q at a distance r is given by the equation:
E = k * (q / r^2)
Where:
E represents the electric field
k is the electrostatic constant (approximately equal to 9 x 10^9 N m^2/C^2)
q is the charge
r is the distance from the charge
Let's calculate the electric fields due to each point charge separately:
For the +1 microcoulomb charge:
E1 = (9 x 10^9 N m^2/C^2) * (1 x 10^-6 C) / (4 cm)^2
For the +4 microcoulomb charge:
E2 = (9 x 10^9 N m^2/C^2) * (4 x 10^-6 C) / (4 cm)^2
Now, since the distance of the null point satisfies the condition that the electric fields due to each point charge are equal in magnitude but opposite in direction, we can set up the following equation:
E1 = -E2
Solving the equation will give us the distance of the null point from the small charge.
Regarding the electric potential at the null point, it will be zero because the null point is a position where the electric field due to the two charges cancels each other out completely.
To find the distance of the null point from the small charge and the electric potential at the null point, we can make use of the concept of electric potential and Coulomb's law.
Step 1: Calculate the electric field due to the +1 microcoulomb charge at the null point.
- The electric field at a point due to a point charge can be calculated using the formula: E = k * (Q / r^2), where E is the electric field, k is Coulomb's constant (8.99 × 10^9 Nm^2/C^2), Q is the charge, and r is the distance to the charge.
- Substituting the given values, E = (8.99 × 10^9) * (1 × 10^-6 / r^2).
Step 2: Calculate the electric field due to the +4 microcoulomb charge at the null point.
- Using the same formula, E = (8.99 × 10^9) * (4 × 10^-6 / (0.04 - r)^2), since the charges are separated by a distance of 4 cm, or 0.04 m.
Step 3: Set the electric fields from the two charges equal to each other to find the distance of the null point (r).
- Set (8.99 × 10^9) * (1 × 10^-6 / r^2) = (8.99 × 10^9) * (4 × 10^-6 / (0.04 - r)^2).
- Simplify the equation and solve for r.
Step 4: Calculate the electric potential at the null point.
- The electric potential at a point due to a point charge can be calculated using the formula: V = k * (Q / r), where V is the electric potential.
- Substituting the known values, V = (8.99 × 10^9) * (1 × 10^-6 / r).
By following these steps, you can find the distance of the null point from the small charge and the electric potential at the null point. Remember to substitute the specific values provided in the problem to get the final result.