search option for 1 to many relationships

I made 1 to many relation ships with school and professor…search option is working for professor but not for school. here are the erorrs and my code…please help—

ActiveRecord::RecordNotFound

in ProfessorsController#index

Couldn't find School without an ID

Rails.root: /home/vmuser/workspace/project3 -3

Application Trace |
Framework Trace |
Full Trace

app/controllers/professors_controller.rb:15:in `index'

codes in controller:
def index

    @school=School.find(params[:id])
      @professor =@school.professors.build
     @professors =Professor.search(params[:search])

end

codes in index:
<%= form_tag professors_path, :method => :get do %>

<%= text_field_tag :search, params[:search] %> <%= submit_tag "Search", :name => nil %> <% end %>