The dimension of electric charge is [M^1 L^2 T^-3 I^1].
Questions & Step-by-step Solutions
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Q
Q: What is the dimension of electric charge?
Solution: The dimension of electric charge is [M^1 L^2 T^-3 I^1].
Steps: 7
Step 1: Understand that dimensions are a way to express physical quantities in terms of basic quantities like mass (M), length (L), time (T), and electric current (I).
Step 2: Electric charge is related to the flow of electric current, which is measured in amperes (A).
Step 3: Recall that current (I) is defined as charge (Q) per unit time (T), so we can express charge in terms of current and time: Q = I * T.
Step 4: From the equation Q = I * T, we can express the dimension of charge as [I^1 T^1].
Step 5: To find the complete dimension of electric charge, we need to relate it to mass (M) and length (L).
Step 6: Using the relationship from electromagnetism, we find that charge can also be expressed in terms of mass, length, and time: [M^1 L^2 T^-3 I^1].
Step 7: Therefore, the dimension of electric charge is [M^1 L^2 T^-3 I^1].
