6. Two charges, Q1 = 4.6x10-9 C and Q2 = 4.3 x10-9 C, are 60mm apart. What is the electric field halfway between them?
To calculate the electric field halfway between the two charges, we can use the formula for electric field due to a point charge. The electric field due to a point charge Q at a distance r is given by:
E = k * |Q| / r²
Where:
E is the electric field,
k is the Coulomb's constant (k = 8.99 x 10^9 N.m²/C²),
Q is the magnitude of the charge, and
r is the distance from the charge.
In this case, we have two charges: Q1 = 4.6 x 10^-9 C and Q2 = 4.3 x 10^-9 C, which are 60 mm apart.
To find the electric field halfway between them, we need to consider the electric fields due to each charge and their directions.
Step 1: Calculate the electric field due to Q1 at the midway point (E1).
Let the distance between Q1 and the midpoint be x, and the total distance between Q1 and Q2 be 60 mm. Therefore, the distance between the midpoint and Q2 is (60 - x) mm.
Electric field due to Q1 at the midpoint (E1) can be calculated by substituting Q = Q1, and r = x, into the formula:
E1 = k * |Q1| / x²
Step 2: Calculate the electric field due to Q2 at the midway point (E2).
Similarly, the electric field due to Q2 at the midpoint (E2) can be calculated by substituting Q = Q2, and r = 60 - x, into the formula:
E2 = k * |Q2| / (60 - x)²
Step 3: Calculate the net electric field at the midpoint (E_net).
Since the electric field is a vector quantity, the net electric field at the midpoint is the vector sum of E1 and E2.
E_net = E1 + E2
Step 4: Combine the magnitudes and directions.
To calculate the magnitude and direction of the electric field halfway between the charges, we can use the principle of superposition. If the magnitudes of E1 and E2 are equal but opposite in direction, their vector sum will give the net electric field at the midpoint.
Therefore, the magnitude of the electric field at the midpoint is the sum of the magnitudes of E1 and E2:
|E_net| = |E1| + |E2|
To find the direction of the electric field at the midpoint, you need to determine if the net electric field points towards Q1 or Q2. The direction is determined by the sign of the charges and their relative positions.
Substitute the values of Q1, Q2, x, and (60 - x) into the formulas for E1 and E2, calculate the magnitudes |E1| and |E2|, and then combine them to find |E_net|. Finally, consider the direction based on the signs of the charges and their relative positions.
Please note that this explanation assumes the charges are point charges, and the distance given is the distance between their centers. If the charges have physical dimensions or the distance given is between their edges, you need to consider the correct distances in the formulas.