A charge of -4.00 nC is located at (0,1.00)m. what is the x-component of the electric field at(4.00,-2.00)m?
E =kq/r^2
for x component find angle tan-1(-2/3)
then E cos(angle)
To calculate the x-component of the electric field at a given point, you can use Coulomb's law. Coulomb's law states that the electric field at a point due to a charged particle is given by:
E = k * (Q / r^2)
Where:
E is the electric field
k is the Coulomb's constant (9 x 10^9 N m^2 / C^2)
Q is the charge of the particle
r is the distance between the charged particle and the point where the electric field is being calculated.
In this case, we have a charge of -4.00 nC located at (0,1.00)m and we want to find the x-component of the electric field at (4.00,-2.00)m.
The distance (r) between the charged particle and the point (4.00,-2.00)m is given by:
r = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((4.00 - 0)^2 + (-2.00 - 1.00)^2)
= sqrt(16 + 9)
= sqrt(25)
= 5.00 m
Now, we can calculate the electric field using Coulomb's law:
E = k * (Q / r^2)
= (9 x 10^9 N m^2 / C^2) * (-4.00 x 10^-9 C) / (5.00 m)^2
Calculating this gives us:
E = -2.88 x 10^6 N/C
Therefore, the x-component of the electric field at (4.00,-2.00)m is -2.88 x 10^6 N/C.
To calculate the x-component of the electric field, we can use Coulomb's law, which states that the electric field created by a point charge is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance from the charge.
The formula for the electric field (E) at a given point due to a point charge (q) is given by:
E = k * (q / r^2)
where:
- E is the electric field
- k is the Coulomb's constant (approximately equal to 9 × 10^9 N m^2/C^2)
- q is the magnitude of the charge
- r is the distance from the charge to the point where the field is measured
In this case, the charge is -4.00 nC, which means the magnitude of the charge is 4.00 nC (since charge is a scalar quantity). The distance from the charge to the point where we want to calculate the electric field is the distance between the two points: (4.00, -2.00)m and (0, 1.00)m.
The x-component of the electric field can be calculated using the formula above by substituting the values:
E_x = k * (q / r^2) * cos(theta)
where:
- E_x is the x-component of the electric field
- k, q, and r are the same as before
- theta is the angle between the axis and the line connecting the charge and the point where the field is measured
In this case, since both points are on the x-axis, the angle theta is zero degrees, and cos(0) = 1. Therefore, we can ignore the cos(theta) in our calculation. Hence, we can calculate the x-component of the electric field at (4.00, -2.00)m as follows:
E_x = k * (q / r^2)
Now let's plug in the values into the equation:
- k = 9 × 10^9 N m^2/C^2
- q = -4.00 nC = -4.00 × 10^-9 C (since 1 nC = 10^-9 C)
- r = distance between the points = sqrt((4.00 - 0)^2 + (-2.00 - 1.00)^2) = sqrt(4^2 + (-3)^2) = sqrt(16 + 9) = sqrt(25) = 5.00 m
E_x = (9 × 10^9 N m^2/C^2) * (-4.00 × 10^-9 C) / (5.00 m)^2
Now calculate the numerator first:
(-4.00 × 10^-9 C) × (9 × 10^9 N m^2/C^2) = -36 × 10^0 N m
Next, calculate the denominator:
(5.00 m)^2 = 25.00 m^2
Now divide the numerator by the denominator:
E_x = (-36 × 10^0 N m) / (25.00 m^2)
Simplifying, we get:
E_x = -1.44 × 10^0 N/C
Therefore, the x-component of the electric field at (4.00, -2.00)m is -1.44 N/C.