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An electric field (\textbf{E}) is a region around a charged particle where a force would be experienced by other charges. In the context of our problem, the electric field needed is to counteract the deflection caused by the magnetic field, ensuring the ion travels straight. When the ion enters the electric field, it feels a force proportional to the charge of the ion times the electric field strength. Mathematically, this is expressed as:
\(F_E = eE\),
where \(e\) is the charge of the ion (for \(^6 Li^\text{+}\), this is \(+e\)). The direction of this force is determined by the direction of the electric field and the sign of the charge. This force ensures that the ion remains undeviated by balancing out the magnetic force.

Magnetic fields (\textbf{B}) exert a force on moving charges, such as ions. When a charged particle moves through a magnetic field perpendicular to its velocity, it experiences a force termed as the Lorentz force. This force acts perpendicular to both the magnetic field direction and the velocity of the particle and is given by:
\(F_B = evB\),
where \(v\) is the velocity of the ion and \(B\) is the magnetic field strength. The magnetic force would normally cause the ion to move in a curved path, but if an electric field is properly applied, this effect can be counteracted.

Potential difference (\textbf{V}) is the difference in electric potential between two points. It tells us how much work is done in moving a charge between those two points. In the exercise, the ions are accelerated by a potential difference of \(10 \text{kV}\). This energy provided to the ions is converted into kinetic energy, calculated using:
\(K.E. = eV\),
where \(e\) is the elementary charge \(1.602 \times 10^{-19}\text{C}\) and \(V\) is the provided potential difference. This kinetic energy gained by the ions plays a crucial role in determining their speed.

Kinetic energy (\textbf{K.E.}) relates to the energy that a body possesses due to its motion. When the ions are accelerated by the potential difference, their kinetic energy can be found using the equation:
\(K.E. = \frac{1}{2} mv^2\),
where \(m\) is the mass of the ion and \(v\) is its velocity. First, we get the kinetic energy from the potential difference formula \(K.E. = eV\), and then relate it to the velocity to find:
\(v = \frac{2eV}{m}\). This velocity is used later to balance the forces of the electric and magnetic fields.

Ion acceleration occurs due to the potential difference applied across the ions, giving them kinetic energy. By accelerating the ions to a known velocity, we can predict their behavior in both electric and magnetic fields. In the exercise, the ions are initially accelerated via a \(10 \text{kV}\) potential difference, contributing directly to their kinetic energy:
\(K.E. = eV\). This acceleration ensures that the ions acquire sufficient velocity to allow analysis of their behavior in the magnetic field:
\(v = \frac{2eV}{m}\). Thus, we can then equate forces due to electric and magnetic fields to find the appropriate electric field strength that balances the magnetic deflection.