Which equation expresses the superposition principle for electric fields?

Which equation expresses the superposition principle for electric fields?

• A. E = ∑ Qi
• B. E = ∑ Ei
• C. E = ∑ Ei^2
• D. E = max(Ei)

Answer: (B)

The total electric field at a point is found by adding up all the individual fields vectorially. This means the net field is the vector sum of each source’s field, because the electric field is a linear, vector quantity. So the expression E = ∑ Ei is the correct way to express this superposition: each Ei is the electric field at the point due to the i-th source, and you add them together, taking into account both magnitude and direction. Practically, this means you add components: Ex = ∑ Exi, Ey = ∑ Eyi, Ez = ∑ Ezi. This works regardless of how many charges there are or where they are located, since fields from different sources simply add up. The other forms don’t capture this behavior: summing charges would give total charge, not the field; squaring the fields relates to energy or intensity rather than the field itself; taking only the maximum field ignores contributions from other sources that still affect the net field.

The total electric field at a point is found by adding up all the individual fields vectorially. This means the net field is the vector sum of each source’s field, because the electric field is a linear, vector quantity. So the expression E = ∑ Ei is the correct way to express this superposition: each Ei is the electric field at the point due to the i-th source, and you add them together, taking into account both magnitude and direction. Practically, this means you add components: Ex = ∑ Exi, Ey = ∑ Eyi, Ez = ∑ Ezi.

This works regardless of how many charges there are or where they are located, since fields from different sources simply add up. The other forms don’t capture this behavior: summing charges would give total charge, not the field; squaring the fields relates to energy or intensity rather than the field itself; taking only the maximum field ignores contributions from other sources that still affect the net field.