The electric field at point P due to a point charge Q a distance R away has magnitude E. In order to double the magnitude of the field at P, you could

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The question describes the electric field at point P due to a single point charge Q located at distance R, with the field magnitude E. The key relationship is E ∝ Q / r^2, so scaling either the charge or the distance affects E.

Option presented: 'double the charge to 2Q.' If Q becomes 2Q while the distance R remains the same, the new field magnitude E' = k(2Q)/R^2 = 2(kQ/R^2) = 2E. This directly achieves the goal of doubling the field.

Why this works: since the distance is fixed, increasing the source strength by a factor of 2 increases the field by the same factor, due to linear dependence on Q in the numerator of the expression E = kQ/r^2.

Why other potential methods (not listed) would also work in principle:
- If you could change the distance, reducing r by a factor of 1/√2 would also double the field, because E ∝ 1/r^2, so E' = E/(1/√2)^2 = E/(1/2) = 2E. This shows there are multiple valid approaches, not just altering the charge.

However, since the only option provided states doubling the charge to 2Q, and that operation indeed yields E' = 2E, this option correctly achieves the requested doubling of the field.

In summary, increasing the source charge to 2Q at the same distance doubles the field at P because E scales linearly with Q when r is constant.

SPHY001 Practice Quiz - Unit 18 | LA058

The electric field at point P due to a point charge Q a distance R away has magnitude E. In order to double the magnitude of the field at P, you could

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