The current through inductance L is given by 

In proton-beam therapy, a high-energy beam of protons is fired at a tumor.  As  the protons stop in the tumor, their kinetic energy breaks apart the tumor’s DNA, thus killing the tumor cells. For one patient, it is desired to deposit 0.11 J of proton energy in the tumor. To create the proton beam, protons are accelerated from rest through a 1.2×104 kV potential difference. What is the total charge of the protons that must be fired at the tumor? 

What potential difference is needed to accelerate a He+ ion (charge +e, mass 4 u) from rest to a speed of 3.5 x 106 m/s? (mass of a proton = 1.67 x 10-27 kg, charge of electron = 1.6 x 10-19 C)

a) How long must a 0.54 mm diameter aluminum wire be to have a 0.56 A current when connected to the terminals of a 1.5 V flashlight battery? (Resistivity of aluminum = 2.8 x 10-8

In proton-beam therapy, a high-energy beam of protons is fired at a tumor.  As  the protons stop in the tumor, their kinetic energy breaks apart the tumor’s DNA, thus killing the tumor cells. For one patient, it is desired to deposit 0.08 J of proton energy in the tumor. To create the proton beam, protons are accelerated from rest through a 8.0×103 kV potential difference. What is the total charge of the protons that must be fired at the tumor? 

What potential difference is needed to accelerate a He+ ion (charge +e, mass 4 u) from rest to a speed of 7.0 x 105 m/s? (mass of a proton = 1.67 x 10-27 kg, charge of electron = 1.6 x 10-19 C)

a) How long must a 0.64 mm diameter aluminum wire be to have a 0.60 A current when connected to the terminals of a 1.5 V flashlight battery? (Resistivity of aluminum = 2.8 x 10-8

a) How long must a 0.56 mm diameter aluminum wire be to have a 0.44 A current when connected to the terminals of a 1.5 V flashlight battery? (Resistivity of aluminum = 2.8 x 10-8

Solve the logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the answer as a decimal rounded to the hundredths place. 

Use the properties of logarithms to simplify: