Practice portal › Electric Charge and Properties › Electric Flux and Gauss's Law

Dimensional formula of electric flux = ________.

Asked in GUJCET 2022; GSEB Board March 2023 · Units and dimensions

• (1) M¹L⁻³T⁻³A⁻¹
• (2) M¹L³T⁻³A¹
• (3) M¹L³T⁻³A⁻¹
• (4) M⁻¹L³T⁻³A⁻¹

Step-by-step solution

Why the other options are wrong

• (1) M¹L⁻³T⁻³A⁻¹ has the sign of the length exponent reversed. Flux is field × area, so the two powers of length from the area add to the one already in [E] and give L³; nothing in EA can put length in the denominator. Sanity check: Φ_E=EA fixes it at M¹L³T⁻³A⁻¹.
• (2) M¹L³T⁻³A¹ puts the current dimension in the numerator. E=F/q keeps the charge in the denominator, so the flux must carry A⁻¹; with A¹ the flux would grow with the test charge used to measure the field, which it does not.
• (4) M⁻¹L³T⁻³A⁻¹ makes the mass exponent negative. The force in E=F/q stands in the numerator, so the mass comes out +1; this option would give the flux the unit kg⁻¹ m³ s⁻³ A⁻¹ instead of N m² C⁻¹.

Reading this solution needs no sign-in. You only sign in to practise against the clock and keep your progress.