Determine the dimensions of the magnetic field B . The relevant equations are F = qE , F = qvB , and B = ₀ I 2 a ; where F is force, q is charge, v is speed, I is current, and a is distance.

Step-by-step solution

Using the formula for magnetic force F = qvB , the magnetic field B is given by B = F qv . The dimensional formula for force F is [MLT⁻²] . The dimensional formula for charge q is [IT] . The dimensional formula for velocity v is [LT⁻¹] . Substituting these dimensions into the expression for B , we get: [B] = [MLT⁻²] [IT][LT⁻¹] [B] = [MLT⁻²] [IL] [B] = [MT⁻²I⁻¹]