'Point charges of 0.26 ìC and 0.79 ìC are placed 0.25 m apart.At what point along the line between them is the electric field zero?'
point charges of .26 iC and .79 ic are placed .25m apart.at what point along the line between then is the elrctric field zero
To find the point along the line between the charges where the electric field is zero, we can use the principle of superposition. According to this principle, the total electric field at any point due to multiple charges can be calculated as the vector sum of the individual electric fields produced by each charge.
In this case, we have two point charges: +0.26 μC and +0.79 μC, placed 0.25 m apart. Let's call the position of the charges as Q1 and Q2, with Q1 being the charge of +0.26 μC and Q2 being the charge of +0.79 μC.
When the electric field is zero at a point between the charges, it means that the electric fields produced by Q1 and Q2 cancel each other out.
To get the electric field at any given point due to a single charge, we can use Coulomb's Law, which states that the electric field (E) produced by a point charge (Q) at a distance (r) is given by:
E = k * Q / r^2
Where k is the electrostatic constant, which is approximately 9 x 10^9 N*m^2/C^2.
Now, let's divide the line between the charges into segments and calculate the electric field at each segment. Since the charges are of the same sign, both electric fields will point in the same direction. Therefore, the two electric fields will cancel each other out when they have equal magnitudes.
Let's assume that the distance from Q1 to the point where the electric field is zero is x. Therefore, the distance from Q2 to the same point will be 0.25 - x.
Now, we can calculate the electric fields produced by Q1 and Q2 at this point using Coulomb's Law:
Electric field due to Q1, E1 = k * Q1 / (x)^2
Electric field due to Q2, E2 = k * Q2 / (0.25 - x)^2
Since we want the electric field to be zero, we equate E1 and E2 and solve for x.
k * Q1 / (x)^2 = k * Q2 / (0.25 - x)^2
Now, we can substitute the given values of Q1 and Q2 into the equation:
(9 x 10^9 N*m^2/C^2) * (0.26 x 10^-6 C) / (x)^2 = (9 x 10^9 N*m^2/C^2) * (0.79 x 10^-6 C) / (0.25 - x)^2
Simplifying the equation further:
(0.26 / x^2) = (0.79 / (0.25 - x)^2
Cross multiply to eliminate the denominators:
0.26 * (0.25 - x)^2 = 0.79 * x^2
Expand and rearrange the equation:
0.26 * ((0.25 - x) * (0.25 - x)) = 0.79 * x * x
0.065 - 0.26x + 0.26x^2 = 0.79x^2
Rearranging the equation further:
0.79x^2 - 0.26x^2 - 0.26x + (0.065) = 0
Combining like terms:
0.53x^2 - 0.26x + (0.065) = 0
Now, we can solve this quadratic equation using various methods such as factoring, completing the square, or using the quadratic formula to find the value of x. Solving this equation will give us the position along the line between the charges where the electric field is zero.
By calculating the roots of the equation, we can determine the two possible positions along the line between the charges where the electric field is zero.