Find the dimensions of
a. electric field E,
magnetic field B and
magnetic permeability `mu_0`
. The relavant equations are
`F=qE, FqvB, and B=(mu_0I)/(2pi alpha),`
where F is force q is charge, `nu` is speed I is current, and `alpha` is distance.

Explanation

To find the dimensions of the electric field (E), magnetic field (B), and magnetic permeability (μ₀), we will use the relevant equations provided.

### Step 1: Find the dimensions of the electric field (E)

1. Start with the equation for force:
\[ F = qE \]
Rearranging gives:
\[ E = \frac{F}{q} \]

2. We know the dimensions of force (F) are:
\[ [F] = M^1 L^1 T^{-2} \]

3. The charge (q) can be expressed in terms of current (I) and time (T):
\[ q = I \cdot T \]
Therefore, the dimensions of charge are:
\[ [q] = A^1 T^1 \]

4. Substitute the dimensions of F and q into the equation for E:
\[ [E] = \frac{[F]}{[q]} = \frac{M^1 L^1 T^{-2}}{A^1 T^1} \]

5. Simplifying this gives:
\[ [E] = M^1 L^1 T^{-3} A^{-1} \]

### Step 2: Find the dimensions of the magnetic field (B)

1. Start with the equation:
\[ F = qvB \]
Rearranging gives:
\[ B = \frac{F}{qv} \]

2. We already have the dimensions for F and q. The velocity (v) can be expressed as distance over time:
\[ v = \frac{L}{T} \]
Therefore, the dimensions of velocity are:
\[ [v] = L^1 T^{-1} \]

3. Substitute the dimensions into the equation for B:
\[ [B] = \frac{[F]}{[q][v]} = \frac{M^1 L^1 T^{-2}}{(A^1 T^1)(L^1 T^{-1})} \]

4. Simplifying this gives:
\[ [B] = M^1 L^0 T^{-2} A^{-1} \]

### Step 3: Find the dimensions of magnetic permeability (μ₀)

1. Use the equation:
\[ B = \frac{\mu_0 I}{2 \pi \alpha} \]
Rearranging gives:
\[ \mu_0 = \frac{B \cdot 2 \pi \alpha}{I} \]

2. The dimensions of α (distance) are:
\[ [\alpha] = L^1 \]

3. Substitute the dimensions into the equation for μ₀:
\[ [\mu_0] = \frac{[B] \cdot [\alpha]}{[I]} = \frac{(M^1 L^0 T^{-2} A^{-1})(L^1)}{A^1} \]

4. Simplifying this gives:
\[ [\mu_0] = M^1 L^1 T^{-2} A^{-2} \]

### Final Results
- Dimensions of electric field (E): \( M^1 L^1 T^{-3} A^{-1} \)
- Dimensions of magnetic field (B): \( M^1 L^0 T^{-2} A^{-1} \)
- Dimensions of magnetic permeability (μ₀): \( M^1 L^1 T^{-2} A^{-2} \)