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The magnetic force on an electron in a magnetic field (F) = q v Bsin\(\theta\) B = 10T, q = 3 x 10\(^7\)m/, \(\theta\) = 60º and q = 1.6 x 10\(^{-19}\)C F = 1.6 x 10\(^{-19}\) x 3 x 10\(^7\) x 10 x sin 60º \(\approxeq\) 4.162 \times 10\(^{-11}\)N

The device for measuring the angle of dip is called a dip circle or declinometer. A dip circle contains a magnetic needle that can move freely, enabling it to align with the Earth's magnetic field. The angle formed between the needle and the horizontal plane represents the angle of dip.

A dynamo converts mechanical energy into electrical energy using the principle of electromagnetic induction, which is a magnetic effect of electric current.

The resultant emergent velocity of a charged ion moving through combined electric and magnetic fields can be derived from the condition where the electric force equals the magnetic force. This gives us the formula for the velocity v: q E = qvB v = \(\frac{E}{B}\) (q will cancel out) NOTE: When both fields are present, for the ion to move without deflection, the electric force must equal the magnetic force.

Maximum primary resistance: An ideal transformer is assumed to have zero resistance in its windings. No flux leakage: This is the key feature of an ideal transformer; all the magnetic flux produced by the primary winding links with the secondary winding. Hysteresis: While hysteresis losses can occur in real transformers due to the magnetic properties of the core material, an ideal transformer assumes no losses. Eddy current: Similar to hysteresis, eddy currents are not present in an ideal transformer, which assumes a perfect core with no energy losses

Hot wire ammeters measure current by detecting the heat produced in a wire due to the electric current flowing through it.

Cuts magnetic flux: According to Faraday's law, when a conductor cuts through magnetic field lines (flux), an e.m.f is induced.

The capacitance of a capacitor is given by: C = \(\frac{Q}{V}\) where Q = quantity of charges, and V = voltage Q = 30c and V = 5v C = \(\frac{Q}{V}\) = C = \(\frac{30}{5}\) = 6 farad

Electric field intensity (E) = \(\frac{\text{force}}{\text{charge}}\) = \(\frac{\text{F}}{\text{q}}\) Given: E = 1200Vm\(^{-1}\), q = 1.6 x 10 \(^{-19}\)C, m = 9.1 x 10\(^{-31}\)kg F = E x q F = 1.6 x 10\(^{-19}\) x 1200 = 1.92 x 10\(^{-16}\)N F = ma a = \(\frac{F}{m}\) = \(\frac{1.92\times 10^{-16}}{9.1\times 10^{-31}}\) \(\approxeq\) 2.11 x 10\(^{14}\)ms\(^{-2}\)

The energy stored in the capacitor = \(\frac{1}{2}\)\(\frac{q^2}{C}\) Where C = 2F, q = 3C = \(\frac{1}{2}\)\(\frac{3^2}{2}\) = \(\frac{9}{4}\) = 2.25J

Electric field intensity(E) = \(\frac{\text{Force}}{\text{charge}}\) = \(\frac{F}{q}\) q = 4\muC = 4.0 x 10\(^{-6}\)C F = 8N E = \(\frac{8}{4.0 \times 10^{-6}}\) = 2.0 x 10\(^6\)NC\(^{-1}\)

Combined capacitance in series = \(\frac{1}{C_T}\) = \(\frac{1}{C_1}\) + \(\frac{1}{C_2}\) The two capacitors have capacitance of 0.0003\muF and 0.0006\muF respectively \(\frac{1}{C_T}\) = \(\frac{1}{0.0003}\) + \(\frac{1}{0.0006}\) = \(\frac{0.0002 + 0.0001}{0.0006}\) \(\frac{1}{C_T}\) = \(\frac{0.0003}{0.0006}\) C\(_T\) = 0.0002\muF.

A voltameter measures the amount of substance that is deposited during electrolysis, allowing for the study of the electrochemical process. It provides information about the quantity of electric charge passed through the electrolyte and the resulting chemical changes. Voltameter is also called an Electrolytic cell.

If a sheet of an insulating material (dielectric) is inserted between the plates of an air capacitor, the capacitance will increase. When a dielectric material is inserted: The permittivity \(\epsilon\) increases (since the permittivity of the dielectric is greater than that of air), This results in an increase in capacitance.

The efficiency of a cell = \(\frac{\text{Ext. R}}{\text{Ext.R + int. r}}\) x 100 Ext. R = X int. r = 2\(\Omega\) Efficiency = 75% = 0.75 0.75 = \(\frac{\text{X}}{\text{X} + 2}\) 0.75( X + 2 ) = X 0.75x + 1.5 = X 0.25X = 1.5 X = \(\frac{1.5}{0.25}\) = 6\(\Omega\)